tag:blogger.com,1999:blog-664211768385279102024-02-07T16:51:10.898-08:00Digital ElectronicsUnknownnoreply@blogger.comBlogger23125tag:blogger.com,1999:blog-66421176838527910.post-78169836788925914342010-09-22T09:04:00.000-07:002010-09-22T09:05:26.111-07:00Numbers with Different Base (Number System)<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} table.MsoTableGrid {mso-style-name:"Table Grid"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; border:solid windowtext 1.0pt; mso-border-alt:solid windowtext .5pt; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-border-insideh:.5pt solid windowtext; mso-border-insidev:.5pt solid windowtext; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> <table class="MsoTableGrid" style="border: medium none ; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody><tr style=""> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 61.15pt;" width="82" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Decimal</p> <p class="MsoNormal" style="text-align: center;" align="center">(base 10)</p> </td> <td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 55.15pt;" width="74" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Binary</p> <p class="MsoNormal" style="text-align: center;" align="center">(base 2)</p> </td> <td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 55.15pt;" width="74" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Octal</p> <p class="MsoNormal" style="text-align: center;" align="center">(base 8)</p> </td> <td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 79.55pt;" width="106" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Hexadecimal</p> <p class="MsoNormal" style="text-align: center;" align="center">(base 16)</p> </td> </tr> <tr style=""> <td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 61.15pt;" width="82" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">00</p> <p class="MsoNormal" style="text-align: center;" align="center">01</p> <p class="MsoNormal" style="text-align: center;" align="center">02</p> <p class="MsoNormal" style="text-align: center;" align="center">03</p> <p class="MsoNormal" style="text-align: center;" align="center">04</p> <p class="MsoNormal" style="text-align: center;" align="center">05</p> <p class="MsoNormal" style="text-align: center;" align="center">06</p> <p class="MsoNormal" style="text-align: center;" align="center">07</p> <p class="MsoNormal" style="text-align: center;" align="center">08</p> <p class="MsoNormal" style="text-align: center;" align="center">09</p> <p class="MsoNormal" style="text-align: center;" align="center">10</p> <p class="MsoNormal" style="text-align: center;" align="center">11</p> <p class="MsoNormal" style="text-align: center;" align="center">12</p> <p class="MsoNormal" style="text-align: center;" align="center">13</p> <p class="MsoNormal" style="text-align: center;" align="center">14</p> <p class="MsoNormal" style="text-align: center;" align="center">15</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 55.15pt;" width="74" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">0000</p> <p class="MsoNormal" style="text-align: center;" align="center">0001</p> <p class="MsoNormal" style="text-align: center;" align="center">0010</p> <p class="MsoNormal" style="text-align: center;" align="center">0011</p> <p class="MsoNormal" style="text-align: center;" align="center">0100</p> <p class="MsoNormal" style="text-align: center;" align="center">0101</p> <p class="MsoNormal" style="text-align: center;" align="center">0110</p> <p class="MsoNormal" style="text-align: center;" align="center">0111</p> <p class="MsoNormal" style="text-align: center;" align="center">1000</p> <p class="MsoNormal" style="text-align: center;" align="center">1001</p> <p class="MsoNormal" style="text-align: center;" align="center">1010</p> <p class="MsoNormal" style="text-align: center;" align="center">1011</p> <p class="MsoNormal" style="text-align: center;" align="center">1100</p> <p class="MsoNormal" style="text-align: center;" align="center">1101</p> <p class="MsoNormal" style="text-align: center;" align="center">1110</p> <p class="MsoNormal" style="text-align: center;" align="center">1111</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 55.15pt;" width="74" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">00</p> <p class="MsoNormal" style="text-align: center;" align="center">01</p> <p class="MsoNormal" style="text-align: center;" align="center">02</p> <p class="MsoNormal" style="text-align: center;" align="center">03</p> <p class="MsoNormal" style="text-align: center;" align="center">04</p> <p class="MsoNormal" style="text-align: center;" align="center">05</p> <p class="MsoNormal" style="text-align: center;" align="center">06</p> <p class="MsoNormal" style="text-align: center;" align="center">07</p> <p class="MsoNormal" style="text-align: center;" align="center">10</p> <p class="MsoNormal" style="text-align: center;" align="center">11</p> <p class="MsoNormal" style="text-align: center;" align="center">12</p> <p class="MsoNormal" style="text-align: center;" align="center">13</p> <p class="MsoNormal" style="text-align: center;" align="center">14</p> <p class="MsoNormal" style="text-align: center;" align="center">15</p> <p class="MsoNormal" style="text-align: center;" align="center">16</p> <p class="MsoNormal" style="text-align: center;" align="center">17</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 79.55pt;" width="106" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> <p class="MsoNormal" style="text-align: center;" align="center">1</p> <p class="MsoNormal" style="text-align: center;" align="center">2</p> <p class="MsoNormal" style="text-align: center;" align="center">3</p> <p class="MsoNormal" style="text-align: center;" align="center">4</p> <p class="MsoNormal" style="text-align: center;" align="center">5</p> <p class="MsoNormal" style="text-align: center;" align="center">6</p> <p class="MsoNormal" style="text-align: center;" align="center">7</p> <p class="MsoNormal" style="text-align: center;" align="center">8</p> <p class="MsoNormal" style="text-align: center;" align="center">9</p> <p class="MsoNormal" style="text-align: center;" align="center">A</p> <p class="MsoNormal" style="text-align: center;" align="center">B</p> <p class="MsoNormal" style="text-align: center;" align="center">C</p> <p class="MsoNormal" style="text-align: center;" align="center">D</p> <p class="MsoNormal" style="text-align: center;" align="center">E</p> <p class="MsoNormal" style="text-align: center;" align="center">F</p> </td> </tr> </tbody></table>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-66421176838527910.post-6411801502328967372010-09-22T09:03:00.000-07:002010-09-22T09:06:18.902-07:00Complements<div style="text-align: justify;"><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> </div><p style="text-align: justify;" class="MsoNormal">Complements are used in digital computers for simplifying the subtraction operation and for logical manipulations. There are two types of complements for each base-r system: (1) the r’s complement and (2) the (r-1)’s complement. When the value of the base is substituted, the two types receive the names 2’s and 1’s complement for binary numbers, or 10’s and 9’s complement for decimal numbers:</p><div style="text-align: justify;"> </div><p style="text-align: justify; font-weight: bold;" class="MsoNormal">The r’s Complement:</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">Given a positive number N in base r with an integer part of n digits, the r’s complement of N is defined as r<sup>n</sup>-N for N≠0 and<span style=""> </span>0 for<span style=""> </span>N=0. The following numerical example will help clarify the definition.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"> </p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 10’s complement of (52520)<sub>10</sub> is 10<sup>5</sup> – 52520 = 47480.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The number of digits in the number is n = 5.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 10’s complement of (0.3267)<sub>10</sub> is 1 – 0.3267 = 0.6733.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">No integer part, so 10<sup>n</sup> = 10<sup>0</sup> = 1.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 10’s complement of (25.639)<sub>10</sub> is 10<sup>2</sup> – 25.639 = 74.361.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 2’s complement of (101100)<sub>2</sub> is (2<sup>6</sup>)<sub>10</sub> – (101100)<sub>2</sub> = (1000000 – 101100)<sub>2</sub> = 010100.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 2’s complement of (0.0110)<sub>2</sub> is (1 – 0.0110)<sub>2</sub> = 0.1010.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"> </p><div style="text-align: justify;"> </div><p style="text-align: justify; font-weight: bold;" class="MsoNormal">The (r – 1)’s Complement:</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">Given a positive number N in base r with an integer part of n digits and a fraction part of m digits, the (r – 1)’s complement of N is defined as r<sup>n</sup> – r<sup>-m</sup> – N. Some numerical examples follow:</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"> </p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 9’s complement of (52520)<sub>10</sub> is (10<sup>5</sup> – 1 – 52520) = 99999 – 52520 = 47479.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">No fraction part, so 10<sup>-m</sup> = 10<sup>0</sup> = 1.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 9’s complement of (0.3267)<sub>10</sub> is (1 – 10<sup>-4</sup> – 0.3267) = 0.9999 – 0.3267 = 0.6732.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">No integer part, so 10<sup>n</sup> = 10<sup>0</sup> = 1.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 9’s complement of (25.639)<sub>10</sub> is (10<sup>2</sup> – 10<sup>-3</sup> – 25.639) = 99.999 – 25.639 = 74.360.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 1’s complement of (101100)<sub>2</sub> is (2<sup>6</sup> – 1)<sub>10</sub> – (101100)<sub>2</sub> = (111111 – 101100)<sub>2</sub> = 010011.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The 1’s complement of (0.0110)<sub>2</sub> is (1 – 2<sup>-4</sup>)<sub>10</sub> – (0.0110)<sub>2</sub> = (0.1111 – 0.0110)<sub>2</sub> = 0.1001.</p>Unknownnoreply@blogger.com4tag:blogger.com,1999:blog-66421176838527910.post-8779550698994840842010-09-22T09:02:00.001-07:002010-09-22T09:03:32.033-07:00Postulates and Theorems of Boolean Algebra<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} table.MsoTableGrid {mso-style-name:"Table Grid"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; border:solid windowtext 1.0pt; mso-border-alt:solid windowtext .5pt; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-border-insideh:.5pt solid windowtext; mso-border-insidev:.5pt solid windowtext; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> <table class="MsoTableGrid" style="border: medium none ; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody><tr style=""> <td style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 137.9pt;" width="184" valign="top"> <p class="MsoNormal">Postulate 2</p> <p class="MsoNormal">Postulate 5</p> <p class="MsoNormal">Theorem 1</p> <p class="MsoNormal">Theorem 2</p> <p class="MsoNormal">Theorem 3, involution</p> <p class="MsoNormal">Postulate 3, commutative</p> <p class="MsoNormal">Theorem 4, associative</p> <p class="MsoNormal">Postulate 4, distributive</p> <p class="MsoNormal">Theorem 5, DeMorgan</p> <p class="MsoNormal">Theorem 6, absorption</p> </td> <td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 130.75pt;" width="174" valign="top"> <p class="MsoNormal">x + 0 = x</p> <p class="MsoNormal">x + x’ = 1</p> <p class="MsoNormal">x + x = x</p> <p class="MsoNormal">x + 1 = 1</p> <p class="MsoNormal">(x’)’ = x</p> <p class="MsoNormal">x + y = y + x</p> <p class="MsoNormal">x + (y + z) = (x + y) + z</p> <p class="MsoNormal">x (y + z) = xy + xz</p> <p class="MsoNormal">(x + y)’ = x’y’</p> <p class="MsoNormal">x + xy = x</p> </td> <td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 123.95pt;" width="165" valign="top"> <p class="MsoNormal">x . 1 = x</p> <p class="MsoNormal">x . x’ = 0</p> <p class="MsoNormal">x . x = x</p> <p class="MsoNormal">x . 0 = 0</p> <p class="MsoNormal"> </p> <p class="MsoNormal">xy =yx</p> <p class="MsoNormal">x(yz) = (xy)z</p> <p class="MsoNormal">x + yz = (x + y)(x + z)</p> <p class="MsoNormal">(xy)’ = x’ + y’</p> <p class="MsoNormal">x(x + y) = x</p> </td> </tr> </tbody></table>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-55103232817260711082010-09-22T09:01:00.000-07:002010-09-22T09:02:17.622-07:00Minterms and Maxterms for three Binary Variables<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} table.MsoTableGrid {mso-style-name:"Table Grid"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; border:solid windowtext 1.0pt; mso-border-alt:solid windowtext .5pt; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-border-insideh:.5pt solid windowtext; mso-border-insidev:.5pt solid windowtext; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> <table class="MsoTableGrid" style="border: medium none ; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"><tbody><tr style=""><td colspan="3" style="border: 1pt solid windowtext; padding: 0in 5.4pt; width: 173.2pt;" width="231" valign="top"><p class="MsoNormal" style="text-align: center;" align="center">Minterms</p> </td> <td colspan="2" style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext -moz-use-text-color; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 140.45pt;" width="187" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Maxterms</p> </td> </tr> <tr style=""> <td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 0.65in;" width="62" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">x<span style=""> </span>y<span style=""> </span>z</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 51.6pt;" width="69" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Term</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 74.8pt;" width="100" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Designation</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 65.65pt;" width="88" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Term</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 74.8pt;" width="100" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">Designation</p> </td> </tr> <tr style=""> <td style="border-style: none solid solid; border-color: -moz-use-text-color windowtext windowtext; border-width: medium 1pt 1pt; padding: 0in 5.4pt; width: 0.65in;" width="62" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">0<span style=""> </span>0<span style=""> </span>0</p> <p class="MsoNormal" style="text-align: center;" align="center">0<span style=""> </span>0<span style=""> </span>1</p> <p class="MsoNormal" style="text-align: center;" align="center">0<span style=""> </span>1<span style=""> </span>0</p> <p class="MsoNormal" style="text-align: center;" align="center">0<span style=""> </span>1<span style=""> </span>1</p> <p class="MsoNormal" style="text-align: center;" align="center">1<span style=""> </span>0<span style=""> </span>0</p> <p class="MsoNormal" style="text-align: center;" align="center">1<span style=""> </span>0<span style=""> </span>1</p> <p class="MsoNormal" style="text-align: center;" align="center">1<span style=""> </span>1<span style=""> </span>0</p> <p class="MsoNormal" style="text-align: center;" align="center">1<span style=""> </span>1<span style=""> </span>1</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 51.6pt;" width="69" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">x’ y’ z’</p> <p class="MsoNormal" style="text-align: center;" align="center">x’ y’ z</p> <p class="MsoNormal" style="text-align: center;" align="center">x’ y<span style=""> </span>z’</p> <p class="MsoNormal" style="text-align: center;" align="center">x’ y<span style=""> </span>z</p> <p class="MsoNormal" style="text-align: center;" align="center">x<span style=""> </span>y’ z’</p> <p class="MsoNormal" style="text-align: center;" align="center">x<span style=""> </span>y’ z</p> <p class="MsoNormal" style="text-align: center;" align="center">x<span style=""> </span>y<span style=""> </span>z’</p> <p class="MsoNormal" style="text-align: center;" align="center">x<span style=""> </span>y<span style=""> </span>z</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 74.8pt;" width="100" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">m<sub>0</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">m<sub>1</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">m<sub>2</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">m<sub>3</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">m<sub>4</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">m<sub>5</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">m<sub>6</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">m<sub>7</sub></p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 65.65pt;" width="88" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">x + y + z</p> <p class="MsoNormal" style="text-align: center;" align="center">x + y + z’</p> <p class="MsoNormal" style="text-align: center;" align="center">x + y’+ z</p> <p class="MsoNormal" style="text-align: center;" align="center">x + y’+ z’</p> <p class="MsoNormal" style="text-align: center;" align="center">x’+ y + z</p> <p class="MsoNormal" style="text-align: center;" align="center">x’+ y + z’</p> <p class="MsoNormal" style="text-align: center;" align="center">x’+ y’+ z</p> <p class="MsoNormal" style="text-align: center;" align="center">x’+ y’+ z’</p> </td> <td style="border-style: none solid solid none; border-color: -moz-use-text-color windowtext windowtext -moz-use-text-color; border-width: medium 1pt 1pt medium; padding: 0in 5.4pt; width: 74.8pt;" width="100" valign="top"> <p class="MsoNormal" style="text-align: center;" align="center">M<sub>0</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">M<sub>1</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">M<sub>2</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">M<sub>3</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">M<sub>4</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">M<sub>5</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">M<sub>6</sub></p> <p class="MsoNormal" style="text-align: center;" align="center">M<sub>7</sub></p> </td> </tr> </tbody></table>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-5879619614908163072010-09-22T05:43:00.000-07:002010-09-22T05:44:35.862-07:00Karnaugh Map (K Map)<div style="text-align: justify;"><a name="Karnaugh">A Karnaugh map provides a pictorial method of grouping together expressions with common factors and therefore eliminating unwanted variables. The Karnaugh map can also be described as a special arrangement of a </a>truth table. </div><p style="text-align: justify;"> The diagram below illustrates the correspondence between the Karnaugh map and the truth table for the general case of a two variable problem.<br /><img src="http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/karintro1.gif" width="341" height="167" /><br />The values inside the squares are copied from the output column of the truth table, therefore there is one square in the map for every row in the truth table. Around the edge of the Karnaugh map are the values of the two input variable. A is along the top and B is down the left hand side. The diagram below explains this:<br /><img src="http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/karintro2.gif" width="366" height="171" /><br />The values around the edge of the map can be thought of as coordinates. So as an example, the square on the top right hand corner of the map in the above diagram has coordinates A=1 and B=0. This square corresponds to the row in the truth table where A=1 and B=0 and F=1. Note that the value in the F column represents a particular function to which the Karnaugh map corresponds. </p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-64069469357697015762010-09-22T05:23:00.000-07:002010-09-22T05:37:55.293-07:00Universal Gate<div style="text-align: justify;"><b><span style="font-size: 16pt; font-family: "NFEEDA+TimesNewRoman,Bold"; color: black;">Universal Gates:</span></b><span style="font-weight: bold;"></span><br /><span style="font-weight: bold;"></span></div><div> </div><p style="text-align: justify;" class="MsoNormal"><span style="font-weight: bold;"></span><span style="color: black;">A universal gate is a gate which can implement any Boolean function without need to use any other gate type.</span></p><p style="text-align: justify;" class="MsoNormal"><span style="color: black;">The NAND and NOR gates are universal gates. </span></p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"><span style="color: black;">In practice, this is advantageous since NAND and NOR gates are economical and easier to fabricate and are the basic gates used in all IC digital logic families. </span></p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"><span style="color: black;">In fact, an AND gate is typically implemented as a NAND gate followed by an inverter not the other way around. </span></p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"><span style="color: black;">Likewise, an OR gate is typically implemented as a NOR gate followed by an inverter not the other way around. </span></p> <p style="text-align: justify;" class="MsoNormal"><b><span style="font-size: 16pt; font-family: "NFEEDA+TimesNewRoman,Bold"; color: black;">NAND Gate is a Universal Gate: </span></b><span style="font-size: 16pt; font-family: "NFEEDA+TimesNewRoman,Bold"; color: black;"></span></p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"><span style="color: black;">To prove that any Boolean function can be implemented using only NAND gates, we will show that the AND, OR, and NOT operations can be performed using only these gates.<br /></span></p><p style="text-align: justify;" class="MsoNormal"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzJFvckV_Y0hFoCmyiuscr_VpjhBlVOtP5A-4oXxJ2LaFzf3n3CsAnH5sxxq1WkFsosMp6KcXuA5bQ_mELVGycndV2wJNv_SOWCY4qjDu-tMB8dUXRSuxtzQdsH3-KoDH2Bw-vMY8GxA/s1600/NAND.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 207px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzJFvckV_Y0hFoCmyiuscr_VpjhBlVOtP5A-4oXxJ2LaFzf3n3CsAnH5sxxq1WkFsosMp6KcXuA5bQ_mELVGycndV2wJNv_SOWCY4qjDu-tMB8dUXRSuxtzQdsH3-KoDH2Bw-vMY8GxA/s400/NAND.bmp" alt="" id="BLOGGER_PHOTO_ID_5519713225478188882" border="0" /></a></p> <p style="text-align: justify;" class="MsoNormal"><b><span style="font-size: 16pt; font-family: "NFEEDA+TimesNewRoman,Bold"; color: black;">NOR Gate is a Universal Gate: </span></b><span style="font-size: 16pt; font-family: "NFEEDA+TimesNewRoman,Bold"; color: black;"></span></p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"><span style="color: black;">To prove that any Boolean function can be implemented using only NOR gates, we will show that the AND, OR, and NOT operations can be performed using only these gates. </span></p> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsmDkmk6Yhk6AD0lpC-JF__Du_C53-HrgkzAkAd9aHNy3gjzCVpXhbrWu08Jt6yQPZkWWgkWSZZII4agEz_F41I1BL5ixDkKQ5dBG0UPkhyphenhyphenPxBQHZyEApxCCvk5z6vZOiqzBJMXiA1yA/s1600/NOR.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 207px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsmDkmk6Yhk6AD0lpC-JF__Du_C53-HrgkzAkAd9aHNy3gjzCVpXhbrWu08Jt6yQPZkWWgkWSZZII4agEz_F41I1BL5ixDkKQ5dBG0UPkhyphenhyphenPxBQHZyEApxCCvk5z6vZOiqzBJMXiA1yA/s400/NOR.bmp" alt="" id="BLOGGER_PHOTO_ID_5519713233622186066" border="0" /></a>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-53916307003216439612010-09-22T01:24:00.000-07:002010-09-22T01:36:08.220-07:00Adder<div style="text-align: justify;"><span style="font-weight: bold;" class="mw-headline">Half adder:</span> </div><p style="text-align: justify;">A <b>half adder</b> is a logical circuit that performs an addition operation on two one-bit binary numbers often written as <span class="texhtml"><i>A</i></span> and <span class="texhtml"><i>B</i></span>. The half adder output is a sum of the two inputs usually represented with the signals <span class="texhtml"><i>C<sub>out</sub></i></span> and <span class="texhtml"><i>S</i></span> where sum=2*Cout+S. Following is the logic table for a half adder:</p> <table class="MsoNormalTable" style="margin-left: 6.75pt; margin-right: 6.75pt;" align="left" border="0" cellpadding="0"> <tbody><tr style=""> <td colspan="2" style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><b>Inputs</b></p> </td> <td colspan="2" style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><b>Outputs</b></p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>A</i></b></span></p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>B</i></b></span></p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>C</i></b></span></p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>S</i></b></span></p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> </tr> </tbody></table> <p class="MsoNormal"><br /></p><p class="MsoNormal"><br /></p><p class="MsoNormal"><br /></p><p class="MsoNormal"><br /></p><p class="MsoNormal"><br /></p><p class="MsoNormal"><br /></p><p class="MsoNormal"><br /></p><p class="MsoNormal"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjquFcN-xklDUx-XbO_Yg1Ua6r1Q8jdjROa4V9SXfi6idNC6XOPLRSEPOkLAV7qq6z4_fgRs1CAqOoAYVxsGmEtOtxVBN1jY86mrcY1-j5hMkOBGhzjKh8iZgm2GZGH7rG7JxZH5deJXA/s1600/Half+Adder+Logic+Diagram.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 180px; height: 100px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjquFcN-xklDUx-XbO_Yg1Ua6r1Q8jdjROa4V9SXfi6idNC6XOPLRSEPOkLAV7qq6z4_fgRs1CAqOoAYVxsGmEtOtxVBN1jY86mrcY1-j5hMkOBGhzjKh8iZgm2GZGH7rG7JxZH5deJXA/s400/Half+Adder+Logic+Diagram.JPG" alt="" id="BLOGGER_PHOTO_ID_5519652479403495522" border="0" /></a></p> <p style="text-align: justify;" class="MsoNormal"><br /></p><p style="text-align: justify;" class="MsoNormal">Example half adder circuit diagram</p><div> </div><p style="text-align: justify;">As an example, a Half Adder can be built with an XOR gate and an AND gate.</p> <pre><span style=""> </span>___________</pre><pre><span style=""> </span>A ------|<span style=""> </span>|</pre><pre><span style=""> </span>|<span style=""> </span>Half<span style=""> </span>|----- S=A(+)B</pre><pre><span style=""> </span>|<span style=""> </span>Adder<span style=""> </span>|</pre><pre><span style=""> </span>|<span style=""> </span>|----- C=A.B</pre><pre><span style=""> </span>B ------|___________|</pre> <h3><span class="mw-headline">Full adder:</span></h3> <p class="MsoNormal"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1DA-vsO9y0KX-vdDlc5vubaFbJemEUHtPgsII7a-0A6fqgB1taTbwhX8dfYjalM0v_r7xwbnRRKLk33NHpTgLhgwaweRaDFXXgSHFuFDggV0bOeMiddUBuypa0wr-PNY11ZtK7FV4LA/s1600/Full+Adder+Block+Diagram.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 200px; height: 172px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1DA-vsO9y0KX-vdDlc5vubaFbJemEUHtPgsII7a-0A6fqgB1taTbwhX8dfYjalM0v_r7xwbnRRKLk33NHpTgLhgwaweRaDFXXgSHFuFDggV0bOeMiddUBuypa0wr-PNY11ZtK7FV4LA/s400/Full+Adder+Block+Diagram.JPG" alt="" id="BLOGGER_PHOTO_ID_5519652456022087666" border="0" /></a></p> <p class="MsoNormal"> </p> <p style="text-align: justify;" class="MsoNormal">Schematic symbol for a 1-bit full adder with <span class="texhtml"><i>C<sub>in</sub></i></span> and <span class="texhtml"><i>C<sub>out</sub></i></span> drawn on sides of block to emphasize their use in a multi-bit adder.</p><div style="text-align: justify;"> </div><p style="text-align: justify;">A <b>full adder</b> is a logical circuit that performs an addition operation on three one-bit binary numbers often written as <span class="texhtml"><i>A</i></span>, <span class="texhtml"><i>B</i></span>, and <span class="texhtml"><i>C<sub>in</sub></i></span>. The full adder produces a two-bit output sum typically represented with the signals <span class="texhtml"><i>C<sub>out</sub></i></span> and <span class="texhtml"><i>S</i></span> where sum=2*Cout+S. The full adder's truth table is:</p> <table class="MsoNormalTable" style="" border="0" cellpadding="0"> <tbody><tr style=""> <td colspan="3" style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><b>Inputs</b></p> </td> <td colspan="2" style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><b>Outputs</b></p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>A</i></b></span></p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>B</i></b></span></p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>C<sub>i</sub></i></b></span></p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>C<sub>o</sub></i></b></span></p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center"><span class="texhtml"><b><i>S</i></b></span></p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">0</p> </td> </tr> <tr style=""> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> <td style="padding: 0.75pt;"> <p class="MsoNormal" style="text-align: center;" align="center">1</p> </td> </tr> </tbody></table> <p style="text-align: justify;">A full adder can be implemented in many different ways such as with a custom transistor-level circuit or composed of other gates. One example implementation is with S=(A(+)B)(+)Cin and Cout=(A.B)+(Cin.(A(+)B)).</p> <p class="MsoNormal"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibNIKTf7Wc3Nz7JdczxIcb53FwC4nyTG-6drmfqcYQrA07IeTlb3JjeWgzuIxMTlv05NkcTy9Y0byF9dP9iDDrj6JiaOd9jlWqyuxYKrhn6i9tnbGAylMu_x3rOo0DTxGZU8P3zGAQCQ/s1600/Full+Adder+Logic+Diagram.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 180px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibNIKTf7Wc3Nz7JdczxIcb53FwC4nyTG-6drmfqcYQrA07IeTlb3JjeWgzuIxMTlv05NkcTy9Y0byF9dP9iDDrj6JiaOd9jlWqyuxYKrhn6i9tnbGAylMu_x3rOo0DTxGZU8P3zGAQCQ/s400/Full+Adder+Logic+Diagram.bmp" alt="" id="BLOGGER_PHOTO_ID_5519652464812111874" border="0" /></a></p> <p class="MsoNormal">Example full adder circuit diagram<br /><b>Inputs: {A, B, Cin} → Outputs: {S, Cout}</b></p> <p class="MsoNormal">Example full adder circuit diagram using only NAND and XOR gates<br /><b>Inputs: {A, B, Cin} → Outputs: {S, Cout}</b></p> <p>In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate without altering the resulting logic. Using only two types of gates is convenient if the circuit is being implemented using simple IC chips which contain only one gate type per chip.</p> <p>A full adder can be constructed from two half adders by connecting <i>A</i> and <i>B</i> to the input of one half adder, connecting the sum from that to an input to the second adder, connecting <i>C<sub>i</sub></i> to the other input and OR the two carry outputs. Equivalently, <i>S</i> could be made the three-bit XOR of <i>A</i>, <i>B</i>, and <i>C<sub>i</sub></i>, and <i>C<sub>o</sub></i> could be made the three-bit majority function of <i>A</i>, <i>B</i>, and <i>C<sub>i</sub></i>.</p> <p class="MsoNormal"> </p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-7777927383416392492010-09-21T23:30:00.000-07:002010-09-21T23:41:46.954-07:00Digital IC Terminology<span style="font-weight: bold;">Current and voltage Parameters:</span><br /><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span>V<sub>IH</sub>(min)-High Level Input Voltage: The minimum voltage level required for a logical 1 at an input. Any voltage below this level will not be accepted as a HIGH by the logic circuit.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span>V<sub>IL</sub>(max)-Low Level Input Voltage: The maximum voltage level required for a logical 0 at an input. Any voltage above this level will not be accepted as a LOW by the logic circuit.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span>V<sub>OH</sub>(min)-High Level Output Voltage: The minimum voltage level at a logic circuit output in the logical 1 state under defined load conditions.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span>V<sub>OL</sub>(max)-Low Level Output Voltage: The maximum voltage level at a logic circuit output in the logical 0 state under defined load conditions.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span>I<sub>IH</sub>(min)-High Level Input Current: The current that flows into an input when a specified high level voltage is applied to that input.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span>I<sub>IL</sub>(max)-Low Level Input Current: The current that flows into an input when a specified low level voltage is applied to that input.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span>I<sub>OH</sub>(min)-High Level Output Current: The current that flows from an output in the logical 1 state under specified load conditions.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span>I<sub>OL</sub>(max)-Low Level Output Current: The current that flows from an output in the logical 0 state under specified load conditions.</p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh561z4AN1P58CH9QGINXzyY54PaeahY9HPRJKZA9ijav8TGUvX413QkHoodhEWdGvGsuzDG2zr84thDyBvicD9u_jDVxht07BOZTr2o0cRPFJiBhJeHSL3gm3VMkA6cahWO9zpUENZ8A/s1600/Noise+Immunity.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 293px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh561z4AN1P58CH9QGINXzyY54PaeahY9HPRJKZA9ijav8TGUvX413QkHoodhEWdGvGsuzDG2zr84thDyBvicD9u_jDVxht07BOZTr2o0cRPFJiBhJeHSL3gm3VMkA6cahWO9zpUENZ8A/s400/Noise+Immunity.bmp" alt="" id="BLOGGER_PHOTO_ID_5519621783868593458" border="0" /></a> <p style="text-align: justify;" class="MsoNormal">The high state noise margin V<sub>NH</sub> is defined as </p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">V<sub>NH</sub>=V<sub>IH</sub>(min)-V<sub>OH</sub>(min)</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The low state noise margin V<sub>NL</sub> is defined as </p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">V<sub>N</sub>L=V<sub>IL</sub>(max)-V<sub>OL</sub>(max)</p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-31508064590351390782010-09-21T13:49:00.001-07:002010-09-21T13:56:35.262-07:00Carry Propagation<div style="text-align: justify;">The addition of two binary numbers in parallel implies that all the bits of the angend and addend are available for computation at the same time. </div><p style="text-align: justify;" class="MsoNormal">As in any combinational ckt, the signal must propagate through the gates before the correct output sum is available in the output terminals.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"><span style=""> </span>A binary parallel adder is a digital function that produces the arithmetic sum of two binary numbers in parallel. It consists of full adders connected in cascade, with the output carry from one full adder connected to the input carry of the next full adder.</p> <p class="MsoNormal" style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuw_dIoVcHgqm3dLlh-0UuinrcBZ72OvxB3Co0EEfi5ke1-mnwNg4jyC2guZ188tL9FMfoaenGPlWx4rEoP7Rf3p0IMB1s0M7Exd5-iZJF1YowDWKpmhMz3dxFDizoiF4etMXiu1U1Tw/s1600/Full+Adder.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 156px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuw_dIoVcHgqm3dLlh-0UuinrcBZ72OvxB3Co0EEfi5ke1-mnwNg4jyC2guZ188tL9FMfoaenGPlWx4rEoP7Rf3p0IMB1s0M7Exd5-iZJF1YowDWKpmhMz3dxFDizoiF4etMXiu1U1Tw/s400/Full+Adder.bmp" alt="" id="BLOGGER_PHOTO_ID_5519473283493973298" border="0" /></a></p> <p class="MsoNormal" style="text-align: justify;">Figure shows the interconnection of 4 full adder (FA) ckts to provide a 4 - bit binary parallel adder. The augend bits of A and the addend bits of B are designated by subscript numbers from right to left, with subscript 1 denoting the low order bit. The carries are connected in a chain through the full adders. The input carry to the adder is C<sub>1</sub> and the output carry is C<sub>5</sub>. The S outputs generate the required sum bits. When the 4 bit full adder ckt is enclosed within an IC package, it has four terminals for the augend bits, four terminals for the addend bits, four terminals for the sum bits, and two terminals for the input and output carries.</p>Unknownnoreply@blogger.com3tag:blogger.com,1999:blog-66421176838527910.post-17769033045872939092010-09-21T13:28:00.001-07:002010-09-21T13:36:16.602-07:00Binary Coded Decimal (BCD) Adder<div style="text-align: justify;">Consider the arithmetic addition of two decimal digits in BCD together with a possible carry from a previous stage. </div><p style="text-align: justify;" class="MsoNormal">Each input digit does not exceed 9, the output sum cannot be greater than 9+9+1=19.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">This adder will from the sum in binary and produce a result which may range from 0 to 19.</p><p class="MsoNormal" style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhngsKDSHJNZAzHGVth33AUKKgZxc9W8V8erjVA0ScPykKYPt81EfT8s8ZBjvJH9q-NNaeVVYtee_3K-Vx7_oXCZruFcfZDQtXtXF3OtQi9f86gJzUv6J508Ps_U997h0OCelI_UHYJMg/s1600/Derivation+of+a+BCD+adder.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 350px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhngsKDSHJNZAzHGVth33AUKKgZxc9W8V8erjVA0ScPykKYPt81EfT8s8ZBjvJH9q-NNaeVVYtee_3K-Vx7_oXCZruFcfZDQtXtXF3OtQi9f86gJzUv6J508Ps_U997h0OCelI_UHYJMg/s400/Derivation+of+a+BCD+adder.bmp" alt="" id="BLOGGER_PHOTO_ID_5519467588941730722" border="0"></a></p> <p class="MsoNormal" style="text-align: justify;"> </p> <p style="text-align: justify;" class="MsoNormal">We found the derivation of a BCD adder, when the binary sum is equal to or less than 1001, the corresponding BCD number is identical.</p><div> </div><p style="text-align: justify;" class="MsoNormal">When the binary sum is greater then 1001, the addition of binary 6(0110) to the binary sum converts it to the correct BCD representation and also produces an output carry as required.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">An output carry can be expressed by the Boolean function: C=K+Z<sub>8</sub>Z<sub>4</sub>+Z<sub>8</sub>Z<sub>2</sub>: When C=1, it is necessary to add 0110 to the binary sum and provide an output carry for the next stage.</p><p class="MsoNormal" style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4TpfNP661Fcvy_W3nymCCnSZmkUETtnqmIA14DGvAy-omlfHaiYrxuWsTdNfU-cueTJcgwaHpKbEDFm5-IIcqyoVG60U1VhkS05Ub0o4wt66m4Krl3Spd25DuImU8I7NFmWvoS2Zn0w/s1600/BCD+Adder.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 234px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4TpfNP661Fcvy_W3nymCCnSZmkUETtnqmIA14DGvAy-omlfHaiYrxuWsTdNfU-cueTJcgwaHpKbEDFm5-IIcqyoVG60U1VhkS05Ub0o4wt66m4Krl3Spd25DuImU8I7NFmWvoS2Zn0w/s400/BCD+Adder.bmp" alt="" id="BLOGGER_PHOTO_ID_5519467582614358818" border="0"></a></p> <div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">A decimal parallel adder that adds n decimal digits needs n BCD adder stages. The output carry one stage must be connected to the input carry of the next higher order stage.</p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-42207074400235261502010-09-21T12:32:00.000-07:002010-09-21T12:35:48.015-07:00Magnitude Comparator<div style="text-align: justify;">A magnitude comparator is a combinational ckt that compares two numbers, A and B, and determines their relative magnitudes. </div><p style="text-align: justify;" class="MsoNormal">The outcomes of the comparison is specified by three binary variables that indicate whether A>B, A=B or A<b.></b.></p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">Consider two numbers A and B, with four digits each A=A<sub>3</sub>A<sub>2</sub>A<sub>1</sub>A<sub>0</sub> and B=B<sub>3</sub>B<sub>2</sub>B<sub>1</sub>B<sub>0</sub></p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">The equivalence function: xi=AiBi+A’iB’i <span style=""> </span>as <span style=""> </span>i=0,1,2,3,….</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">If<span style=""> </span>(A=B)=x<sub>3</sub>x<sub>2</sub>x<sub>1</sub>x<sub>0</sub></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify;">(A>B)=A<sub>3</sub>B’<sub>3</sub>+x<sub>3</sub>A<sub>2</sub>B’<sub>2</sub>+x<sub>3</sub>x<sub>2</sub>A<sub>1</sub>B’<sub>1</sub>+x<sub>3</sub>x<sub>2</sub>x<sub>1</sub>A<sub>0</sub>B’<sub>0</sub></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify;">(A<b)=a’><sub>3</sub>B<sub>3</sub>+x<sub>3</sub>A’<sub>2</sub>B<sub>2</sub>+x<sub>3</sub>x<sub>2</sub>A’<sub>1</sub>B<sub>1</sub>+x<sub>3</sub>x<sub>2</sub>x<sub>1</sub>A’<sub>0</sub>B<sub>0</sub></b)=a’></p><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSeGrfjcKwQ7JWxB71bEH6UVtdBzIZYatOJivwbhkmkLRguUN8dR11olSc2_V_QU8k48S76tyHtf2eXxhF74mI7eLWBszKOmvPtgqyyKoHT2Th5Yok-Rma8mxq49OHZhyOYMb3Z3-cGA/s1600/Magnitude+Comparator.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 279px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSeGrfjcKwQ7JWxB71bEH6UVtdBzIZYatOJivwbhkmkLRguUN8dR11olSc2_V_QU8k48S76tyHtf2eXxhF74mI7eLWBszKOmvPtgqyyKoHT2Th5Yok-Rma8mxq49OHZhyOYMb3Z3-cGA/s400/Magnitude+Comparator.bmp" alt="" id="BLOGGER_PHOTO_ID_5519452594484293810" border="0" /></a></p><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"></p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-30902057784019567362010-09-21T11:35:00.000-07:002010-09-21T11:41:42.779-07:00Decoder<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> <p style="text-align: justify;" class="MsoNormal">A decoder is a combinational ckt that converts binary information from n input lines to a maximum of 2<sup>n</sup> unique output lines.</p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal">If the n-bit decoded information has unused or don’t care combinations, the decoder output will have less than 2<sup>n</sup> outputs.</p> <p class="MsoNormal" style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvYq_rloo4yrvYPBkkQ2OG5UIKUGy5BG89FBQ3cOFixO8t87GW5uT9ks7rMx3pmTG4km46nN5bSlFdU70wzTZnIrnkX5r10RcXOr19p_9g8cY_TjVVyd3EI-vD9p_fxCAIvDSc-hFKCg/s1600/Decoder+Truth+Table.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 270px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvYq_rloo4yrvYPBkkQ2OG5UIKUGy5BG89FBQ3cOFixO8t87GW5uT9ks7rMx3pmTG4km46nN5bSlFdU70wzTZnIrnkX5r10RcXOr19p_9g8cY_TjVVyd3EI-vD9p_fxCAIvDSc-hFKCg/s400/Decoder+Truth+Table.bmp" alt="" id="BLOGGER_PHOTO_ID_5519438107147010546" border="0" /></a></p><p class="MsoNormal" style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNBlc2sO8fgDSgIg93hURiY92DZ_hbS0FgYKIK5unrut0plQXs3_L4LtibF7UwrH_q7q0rTMrO79JTbIZEESU0x5F7b5o_mFnO5yrfsdLctxFdYVOXUMVthAEPJUVmJKCeKlmumXFDZQ/s1600/Decoder+ckt+Diagram.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 350px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNBlc2sO8fgDSgIg93hURiY92DZ_hbS0FgYKIK5unrut0plQXs3_L4LtibF7UwrH_q7q0rTMrO79JTbIZEESU0x5F7b5o_mFnO5yrfsdLctxFdYVOXUMVthAEPJUVmJKCeKlmumXFDZQ/s400/Decoder+ckt+Diagram.bmp" alt="" id="BLOGGER_PHOTO_ID_5519438105707603874" border="0" /></a></p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-59668240648035753082010-09-21T10:47:00.000-07:002010-09-21T11:42:05.617-07:00Encoder<div style="text-align: justify;">An encoder is a digital function that produces a reverse operation from that of a decoder. An encoder has 2<sup>n</sup>(or less) input lines and n output lines. The output lines generate the binary code for the 2<sup>n</sup> input variables.</div><p class="MsoNormal" style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0O4LSCbt5VnJYl-3yOQsITQdgS17GjUPv1U7N2656UteFLf7qh-tP14FOkQUsjMJV2InMUxyA-0ImA4L8S87Aya6S_S3EgR1Bu7ZXKGsidRldj19yvYONe5MYc3OOcw-5uezxltKOHg/s1600/Encoder+Truth+Table.bmp"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 270px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0O4LSCbt5VnJYl-3yOQsITQdgS17GjUPv1U7N2656UteFLf7qh-tP14FOkQUsjMJV2InMUxyA-0ImA4L8S87Aya6S_S3EgR1Bu7ZXKGsidRldj19yvYONe5MYc3OOcw-5uezxltKOHg/s400/Encoder+Truth+Table.bmp" alt="" id="BLOGGER_PHOTO_ID_5519438342239317266" border="0" /></a></p> <p class="MsoNormal" style="text-align: justify;">We found from truth table x=D4+D5+D6+D7; y=D2+D3+D6+D7; z=D1+D3+D5+D7</p><p class="MsoNormal" style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-IdYd_YdHlX710uAAaBzZnzj6r5pHV0iV4fknQmeC5uAtAYhwnO0vEWQ-SIi1EzX5_WWZEk8_xcDG32g2mOOXE5V66g8GWvSuyG_RKZRc39cu6sh4HCYKWTVzF3sewCdID12n9-UkQg/s1600/Encoder.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 153px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-IdYd_YdHlX710uAAaBzZnzj6r5pHV0iV4fknQmeC5uAtAYhwnO0vEWQ-SIi1EzX5_WWZEk8_xcDG32g2mOOXE5V66g8GWvSuyG_RKZRc39cu6sh4HCYKWTVzF3sewCdID12n9-UkQg/s400/Encoder.JPG" alt="" id="BLOGGER_PHOTO_ID_5519425415863692434" border="0" /></a></p> <p class="MsoNormal" style="text-align: justify;">D<sub>0</sub> is not connected to any OR gate; the binary output must be all 0’s in this case.</p> <p class="MsoNormal" style="text-align: justify;">The ckt has 8 inputs and could have 2<sup>8</sup>=256 possible input combinations. Only 8 of these combinations have any meaning. The other inputs combinations are don’t care conditions.</p>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-66421176838527910.post-30441118537766018872010-09-21T07:37:00.000-07:002010-09-21T07:44:40.087-07:00Multiplexer<div style="text-align: justify;">Multiplexing means transmitting a large number of information units over a smaller number of channels or lines. A digital multiplexer is a combinational ckt that selects binary information from one of many input lines and directs it to a single output line. The selection of a particular input line is controlled by a set of a selection lines. There are 2n input lines and n selection lines whose bit combinations determine which input is selected. </div><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLZY6ASkkHe6CkcM0r6vY-ZIpPiePQqxsM_w8XheyO8r2p49DmoHznLPv_KqHkjrMkE9fksyV-N9vT5FRmRkrcEuz0N2woEO4EpzXksFXJkCr4TMuFsEDTonYVXK4GVGh8yrs_1iptEQ/s1600/Multiplexer.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 262px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLZY6ASkkHe6CkcM0r6vY-ZIpPiePQqxsM_w8XheyO8r2p49DmoHznLPv_KqHkjrMkE9fksyV-N9vT5FRmRkrcEuz0N2woEO4EpzXksFXJkCr4TMuFsEDTonYVXK4GVGh8yrs_1iptEQ/s400/Multiplexer.JPG" alt="" id="BLOGGER_PHOTO_ID_5519376988775422898" border="0" /></a></p><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> <p class="MsoNormal" style="text-align: justify;">A in decoders, multiplexer ICs may have an enable input to control the operation of the unit. When the enable input is in a given binary state, the outputs are disabled, and when it is in the other state (the enable state), the ckt functions as a normal multiplexer. The enable input can be used to expand two or more multiplexer ICs to a digital multiplexer with a larger number of inputs.</p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-53057840564827142792010-09-21T04:40:00.000-07:002010-09-21T04:48:52.139-07:00Demultiplxer<span style="font-family: Symbol;"><span style="">·<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> </span></span></span>A decoder with an enable input can function as a demultiplexer. A demultiplexer is a ckt that receives information on a single line and transmits this information on one of 2n possible output lines. <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Symbol;"><span style="">·<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> </span></span></span>A decoder with an enable input is referred to as a demultiplexer. It is the enable input that makes the ckt a demultiplexer.</p><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy6NrO5ryU-nCfPdKv5tweHyZVAUXBKgbkA-wdC0-FtIJsxt3T8uL4dIELpAUN16f6zTO4y4qr_SLrEiCeF-nUatQUYlCgAQ8jE-zM7H4P1pH_twoHZvlh8yOL0lKrH6xebZNemirQPA/s1600/Demultiplxer+1.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 198px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy6NrO5ryU-nCfPdKv5tweHyZVAUXBKgbkA-wdC0-FtIJsxt3T8uL4dIELpAUN16f6zTO4y4qr_SLrEiCeF-nUatQUYlCgAQ8jE-zM7H4P1pH_twoHZvlh8yOL0lKrH6xebZNemirQPA/s400/Demultiplxer+1.JPG" alt="" id="BLOGGER_PHOTO_ID_5519330752218623810" border="0" /></a></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Symbol;"><span style=""><span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"></span></span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8F2Fuvsab_21ZPCRbMIes4V24AGQiv_X7SllaoO_vCWBIOQh2YskEnsZnhZfh0uaNpvcD4hAatbKDFputipXnkYdpXqtnFDKnWQnPZJ60-BS_FPoumoNWiIUZ5PmjGBpeJ4NRug_Ofw/s1600/Demultiplxer+2.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 234px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8F2Fuvsab_21ZPCRbMIes4V24AGQiv_X7SllaoO_vCWBIOQh2YskEnsZnhZfh0uaNpvcD4hAatbKDFputipXnkYdpXqtnFDKnWQnPZJ60-BS_FPoumoNWiIUZ5PmjGBpeJ4NRug_Ofw/s400/Demultiplxer+2.JPG" alt="" id="BLOGGER_PHOTO_ID_5519330741225274642" border="0" /></a></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in;"><span style="font-family: Symbol;"><span style="">·<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> </span></span></span>If E is 0 then one demultiplexer is enabled and the other is disabled and for E is 1 then vice-versa.</p>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-42617535911964533192010-09-20T06:37:00.000-07:002010-09-21T04:39:54.203-07:00Read Only Memory (ROM)<div style="text-align: justify;"><span style="font-family: Symbol;"><span style="">·<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> </span></span></span>A ROM is a device that includes both the decoder and the OR gates with in a single IC package. </div><p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in; text-align: justify;"><span style="font-family: Symbol;"><span style="">·<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> </span></span></span>Block diagram shows, n inputs lines, each bit is called an address and m output lines, each bit is called a word.</p> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiF6H5dIuNKKHcD3Njk8_NGs8F91QLVjLBlYH0aB8kbxBhFRryw6OAfVS43Kb5z-jTttBO81Fv_79zXx58OueCO7SIrbGXadH-5vGxtl3woIAu7LoAbEhmdAWXKi0iUHvzwomJGtYsDmg/s1600/ROM.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 217px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiF6H5dIuNKKHcD3Njk8_NGs8F91QLVjLBlYH0aB8kbxBhFRryw6OAfVS43Kb5z-jTttBO81Fv_79zXx58OueCO7SIrbGXadH-5vGxtl3woIAu7LoAbEhmdAWXKi0iUHvzwomJGtYsDmg/s400/ROM.JPG" alt="" id="BLOGGER_PHOTO_ID_5519329249450018690" border="0" /></a> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in; text-align: justify;"><span style="font-family: Symbol;"><span style="">·<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> </span></span></span>The ROM is very often used to implement a complex combinational ckt in one IC package.</p><div> </div><p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in; text-align: justify;"><span style="font-family: Symbol;"><span style="">·<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> </span></span></span>A ROM is essentially a memory device in which a fixed set of binary information is stored.</p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in; text-align: justify;"><span style="font-family: Symbol;"><span style="">·<span style="font-family: "Times New Roman"; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"> </span></span></span>ROMs have many important applications in the design of digital computer systems.</p>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-66421176838527910.post-21082060030704951502010-09-16T06:05:00.000-07:002010-09-20T06:33:16.408-07:00Programmable Logic Array (PLA)<div style="text-align: justify;"><div style="text-align: justify;"><span style=";font-family:Symbol;font-size:100%;" ><span style="">·<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">PLA is similar to a ROM in concept, but the PLA does not provide full decoding of the variables and does not generate all the minterms as in the </span><span style="font-size:100%;">ROM.</span><span style="font-size:100%;"> In PLA, the decoder is replaced by a group of AND gates.</span><br /><span style=";font-family:Symbol;font-size:100%;" ><span style="">·<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">PLA consists of n inputs, m (OR gate) outputs, K (AND gate) product terms and m sum terms.</span><br /><span style=";font-family:Symbol;font-size:100%;" ><span style="">·<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">The PAL is the opposite of the ROM, having a programmable set of ANDs combined with fixed ORs.</span><br /><span style=";font-family:Symbol;font-size:100%;" ><span style="">·<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">Compared to a ROM and a PAL, a PLA is the most flexible having a programmable set of ANDs combined with a programmable set of<span style=""> </span>ORs.</span><br /></div><div style="text-align: justify;"><span style="font-size:100%;"><b>Advantages:</b></span> </div></div><p class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in; text-align: justify;"><span style=";font-family:";font-size:100%;" ><span style="">o<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">A PLA can have large N and M permitting implementation of<span style=""> </span>equations that are impractical for a ROM (because of the number of inputs, N, required </span></p><div> </div><p class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in; text-align: justify;"><span style=";font-family:";font-size:100%;" ><span style="">o<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">A PLA has all of<span style=""> </span>its product terms connectable to all outputs, overcoming the problem of<span style=""> </span>the limited inputs to the PAL Ors</span></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in; text-align: justify;"><span style=";font-family:";font-size:100%;" ><span style="">o<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">Some PLAs have outputs that can be complemented, adding POS functions</span></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-size:100%;"> </span></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-size:100%;"><b>Disadvantages:</b></span></p><div> </div><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify;"><span style="font-size:100%;"> </span></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in; text-align: justify;"><span style=";font-family:";font-size:100%;" ><span style="">o<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">Often, the product term count limits the application of a PLA.</span></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in; text-align: justify;"><span style=";font-family:";font-size:100%;" ><span style="">o<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">Two-level multiple-output optimization is required to reduce<span style=""> </span>the number of product terms in an implementation, helping to fit it into a PLA.</span></p><div style="text-align: justify;"> </div><p class="MsoNormal" style="margin-left: 1in; text-indent: -0.25in; text-align: justify;"><span style=";font-family:";font-size:100%;" ><span style="">o<span style=";font-family:";" > </span></span></span><span style="font-size:100%;">Multi-level circuit capability available in PAL not available in PLA.<span style=""> </span>PLA requires external connections to do multi-level circuits.</span></p><div style="text-align: justify;"> </div><p style="text-align: justify;" class="MsoNormal"><br /></p><p style="text-align: justify;" class="MsoNormal"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVpsBnPph7P24LOm-dv9cMvfj8H32oA82CI4AeGxtWJ7qg6n3dcjrEil23tjqmcSlWwhu5YjENVIkyEusStrNlBzu7BvdRD7WY88cvXb-tTcSLmFezuPBBMqKtyTlN-LjQzn3_22zNLA/s1600/PLA.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 284px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVpsBnPph7P24LOm-dv9cMvfj8H32oA82CI4AeGxtWJ7qg6n3dcjrEil23tjqmcSlWwhu5YjENVIkyEusStrNlBzu7BvdRD7WY88cvXb-tTcSLmFezuPBBMqKtyTlN-LjQzn3_22zNLA/s400/PLA.JPG" alt="" id="BLOGGER_PHOTO_ID_5518987031794810002" border="0" /></a></p><p style="text-align: justify;" class="MsoNormal"><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> </p><p style="text-align: justify;" class="MsoNormal"><span style="font-size:100%;">3-input, 3-output PLA with 4 product terms.</span></p>Unknownnoreply@blogger.com4tag:blogger.com,1999:blog-66421176838527910.post-59408774284725458412010-09-16T05:29:00.000-07:002010-09-16T06:06:32.173-07:00The IC Digital Logic Families<span style="font-weight: bold;">The IC Digital Logic Families:</span>
<br /><meta equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 10"><meta name="Originator" content="Microsoft Word 10"><link rel="File-List" href="file:///C:%5CDOCUME%7E1%5CRashad%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml"><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><style> <!-- /* Font Definitions */ @font-face {font-family:Wingdings; panose-1:5 0 0 0 0 0 0 0 0 0; mso-font-charset:2; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:0 268435456 0 0 -2147483648 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"; mso-bidi-language:BN; mso-no-proof:yes;} @page Section1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.Section1 {page:Section1;} /* List Definitions */ @list l0 {mso-list-id:397479676; mso-list-type:hybrid; mso-list-template-ids:205148846 67698689 67698691 67698693 67698689 67698691 67698693 67698689 67698691 67698693;} @list l0:level1 {mso-level-number-format:bullet; mso-level-text:; mso-level-tab-stop:.25in; mso-level-number-position:left; margin-left:.25in; text-indent:-.25in; font-family:Symbol;} @list l1 {mso-list-id:1176965276; mso-list-type:hybrid; mso-list-template-ids:-571559944 67698689 67698691 67698693 67698689 67698691 67698693 67698689 67698691 67698693;} @list l1:level1 {mso-level-number-format:bullet; mso-level-text:; mso-level-tab-stop:.25in; mso-level-number-position:left; margin-left:.25in; text-indent:-.25in; font-family:Symbol;} ol {margin-bottom:0in;} ul {margin-bottom:0in;} --> </style><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->RTL-Resistor-Transistor Logic.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->DTL-Diode-Transistor Logic.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->I2L-Integrated-Injection Logic.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->TTL-Transistor-Transistor Logic.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->ECL-Emitter-Coupled Logic.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->MOS-Metal-Oxide Semi-conductor.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->CMOS-Complementary Metal-Oxide Semi-conductor.</p> <p class="MsoNormal"><o:p> </o:p></p> <p style="font-weight: bold;" class="MsoNormal">Advantage of CMOS:</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->Ckt is must simpler.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->Easy to fabricate.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->Faster.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->Power consumption is low.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><!--[if !supportLists]--><span style="font-family:Symbol;"><span style="">·<span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->Comparatively cheeper.</p> <p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style=""><span style=";font-family:";font-size:7pt;" >
<br /></span></span></span></p><p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-family:Symbol;"><span style=""><span style=";font-family:";font-size:7pt;" > </span></span></span><!--[endif]-->
<br /></p><p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><span style="font-weight: bold;">Disadvantage</span> of CMOS is the logic is always invert.</p><p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;">
<br /></p><p class="MsoNormal" style="margin-left: 0.25in; text-indent: -0.25in;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXF1aSyuiau_-sOAPVI5MpFaBFKsNK2Tvb8UIE9pbIAJRGbhI0PZtpbSNLh991w9B3eM0TS6wOrCUZEnPDippqsXMygBvjGkpCOTPx6Vy9jg6KOrN23FE_JqKeKtBjLe8P74Mmrm4y2g/s1600/CMOS+Logic+Ckt.JPG"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px; height: 109px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXF1aSyuiau_-sOAPVI5MpFaBFKsNK2Tvb8UIE9pbIAJRGbhI0PZtpbSNLh991w9B3eM0TS6wOrCUZEnPDippqsXMygBvjGkpCOTPx6Vy9jg6KOrN23FE_JqKeKtBjLe8P74Mmrm4y2g/s400/CMOS+Logic+Ckt.JPG" alt="" id="BLOGGER_PHOTO_ID_5517495830510994322" border="0" /></a></p>
<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-68750170172440004832010-08-14T09:21:00.000-07:002010-08-14T09:45:01.475-07:00Flip Flop<div style="text-align: justify;"><span style="font-size:100%;">"Flip-flop" is the common name given to two-state devices which offer basic memory for sequential logic operations. Flip-flops are heavily used for digital data storage and transfer and are commonly used in banks called "registers" for the storage of binary numerical data.</span><br /></div><center><img src="http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/ietron/flipflop.gif" usemap="#mic" /><br /><br /><br /><div style="text-align: left;"><h2><span class="editsection"></span> <span style="font-size:100%;"><span class="mw-headline" id="RS_.28Reset-Set.29_flip-flop">RS (Reset-Set) flip-flop:</span></span></h2><div style="text-align: justify;">The fundamental latch is the simple <i>RS flip-flop</i> (also commonly known as <i>SR flip-flop</i>), where R and S stand for <i>reset</i> and <i>set</i>, respectively. It can be constructed from a pair of cross-coupled <span class="mw-redirect">NAND</span> or NOR logic gates. The stored bit is present on the output marked Q. </div><p style="text-align: justify;">Normally, in storage mode, the R and S inputs are both low, and feedback maintains the Q and <span style="text-decoration: overline;">Q</span> outputs in a constant state, with <span style="text-decoration: overline;">Q</span> the complement of Q. If S is pulsed high while R is held low, then the Q output is forced high, and stays high even after S returns low; similarly, if R is pulsed high while S is held low, then the Q output is forced low, and stays low even after R returns low.</p><div style="text-align: justify;"> </div><p style="text-align: justify;">The next-state equation of the RS flip-flop is</p><div style="text-align: justify;"> </div><dl style="text-align: justify;"><dd><img class="tex" alt="Q_{next} = S + \overline{R}Q" src="http://upload.wikimedia.org/math/1/1/3/1131c952809cf7dc0b1dc80dddfe47d8.png" /></dd></dl><div style="text-align: justify;"> where Q is the current state. <span class="texhtml"><i>Q</i><sub><i>n</i><i>e</i><i>x</i><i>t</i></sub></span> becomes Q (the stored value) at clock edge.<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOsd9iEo3OQqIwAfPQKcuUcWqqRZKnDGFrmWkQylgDzm95vY953KCEwdMTfqkiV5Io0dNTdZ5Sr1PIv1LUhCFBxKMd35VBgo69tkVT5BWP3VD9CTpYa5YemPysTKB4FjkgbdHgkwSo4Q/s1600/Flip-Flop.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 292px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOsd9iEo3OQqIwAfPQKcuUcWqqRZKnDGFrmWkQylgDzm95vY953KCEwdMTfqkiV5Io0dNTdZ5Sr1PIv1LUhCFBxKMd35VBgo69tkVT5BWP3VD9CTpYa5YemPysTKB4FjkgbdHgkwSo4Q/s400/Flip-Flop.gif" alt="" id="BLOGGER_PHOTO_ID_5505307051271316914" border="0" /></a><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><table class="wikitable" style="text-align: center;"><tbody><tr><th colspan="8">RS Flip-Flop operation (BUILT WITH NOR GATES) <sup id="cite_ref-manokime_7-0" class="reference"><a href="http://en.wikipedia.org/wiki/Flip-flop_%28electronics%29#cite_note-manokime-7"><span></span><span></span></a></sup></th> </tr> <tr> <th colspan="3">Characteristic table</th> <th colspan="5">Excitation table</th> </tr> <tr> <th>S</th> <th>R</th> <th>Action</th> <th>Q(t)</th> <th>Q(t+1)</th> <th>S</th> <th>R</th> <th>Action</th> </tr> <tr> <td>0</td> <td>0</td> <td>Keep state</td> <td>0</td> <td>0</td> <td>0</td> <td>X</td> <td>No change</td> </tr> <tr> <td>0</td> <td>1</td> <td>Q = 0</td> <td>1</td> <td>0</td> <td>0</td> <td>1</td> <td>reset</td> </tr> <tr> <td>1</td> <td>0</td> <td>Q = 1</td> <td>0</td> <td>1</td> <td>1</td> <td>0</td> <td>set</td> </tr> <tr> <td>1</td> <td>1</td> <td><span class="mw-redirect">Race Condition</span></td> <td>1</td> <td>1</td> <td>X</td> <td>0</td> <td>No Change</td></tr></tbody></table><br /></div></div></center>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-45719252226324157362010-08-14T05:17:00.000-07:002010-08-14T09:36:33.938-07:00The D Flip-Flop<div style="text-align: justify;">The D flip-flop tracks the input, making transitions with match those of the input D. The D stands for "data"; this flip-flop stores the value that is on the data line. It can be thought of as a basic memory cell. A D flip-flop can be made from a set/reset flip-flop by tying the set to the reset through an inverter. The result may be clocked.<br /><br /></div><div style="text-align: justify;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmPd2xZe2Oqxm_u1MOe-6VReDQQ9xmFAMbbHeC6mOA3SuThKDdmIK2Pbx4TMV-NBjqa2ZxXRmGpVeRZa6vfLhg3fwHo3gE6DGDz5ERMbbIJzN9HZ084D6cs91f1Fw6_iG-NL882xm7hg/s1600/D+Flip-Flop.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 128px; height: 110px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmPd2xZe2Oqxm_u1MOe-6VReDQQ9xmFAMbbHeC6mOA3SuThKDdmIK2Pbx4TMV-NBjqa2ZxXRmGpVeRZa6vfLhg3fwHo3gE6DGDz5ERMbbIJzN9HZ084D6cs91f1Fw6_iG-NL882xm7hg/s400/D+Flip-Flop.gif" alt="" id="BLOGGER_PHOTO_ID_5505300621660226850" border="0" /></a><br /><br /><h1 style="text-align: justify;"><br /></h1><span style="font-weight: bold;font-size:100%;" ><br /><br /><br /><br /><br /><br />Clocked D Flip-Flop:<br /><br /></span><div style="text-align: justify;"><span style="font-size:100%;">Clocked D Flip-Flop:</span>A D flip-flop constructed from a NAND-latch .<br /><br /></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbD4iKKmJIgRHTWQDSAu_r-88o21s0BUUpaudw7_ZI4M1ipkvUIjFa0U_X1GCvht03XgljRTjuaFwE5t3UPSA-RZQHRvCggaPYbVs0yw_qBFmlSDuRD8ZBT4jmCaskjZP63gWlDZLDtg/s1600/Clocked+D+Flip-Flop.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 216px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbD4iKKmJIgRHTWQDSAu_r-88o21s0BUUpaudw7_ZI4M1ipkvUIjFa0U_X1GCvht03XgljRTjuaFwE5t3UPSA-RZQHRvCggaPYbVs0yw_qBFmlSDuRD8ZBT4jmCaskjZP63gWlDZLDtg/s400/Clocked+D+Flip-Flop.gif" alt="" id="BLOGGER_PHOTO_ID_5505300615527353634" border="0" /></a><br /><h1 style="text-align: left;"><br /></h1><h1 style="text-align: left;"><br /></h1><h1 style="text-align: left;"><br /></h1><h1 style="text-align: justify;"><br /></h1><h1 style="text-align: justify;"><br /></h1><h1 style="text-align: justify;"><br /></h1><h1 style="text-align: justify;"><span style="font-size:100%;">D Flip-Flop from NAND Latch:</span></h1><div style="text-align: justify;"> The output Q will track the input D so long as the flip-flop remains enabled.<br /><br /></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMfIXur_qZgM3A0c0i3MMG7ck62S5QIqSzFpqEF32417-B1ukurLNAkG7gOqgR0qT7azMigjgqSWZkRUAiw48q0g6l3PR6W9NxIL7sza2Rdb7YHsBJPdfoxy6US_-4tlkDofbwzxph-w/s1600/D+Flip+Flop+NAND.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 398px; height: 256px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMfIXur_qZgM3A0c0i3MMG7ck62S5QIqSzFpqEF32417-B1ukurLNAkG7gOqgR0qT7azMigjgqSWZkRUAiw48q0g6l3PR6W9NxIL7sza2Rdb7YHsBJPdfoxy6US_-4tlkDofbwzxph-w/s400/D+Flip+Flop+NAND.gif" alt="" id="BLOGGER_PHOTO_ID_5505300616809867586" border="0" /></a><br /><h1 style="text-align: left;"><br /></h1><h1 style="text-align: left;"><br /></h1><h1 style="text-align: left;"><br /></h1><h1 style="text-align: left;"><br /></h1><h1 style="text-align: justify; font-weight: bold;"><br /></h1><h1 style="text-align: justify; font-weight: bold;"><br /></h1><h1 style="text-align: justify; font-weight: bold;"><br /></h1><h1 style="text-align: justify; font-weight: bold;"><br /></h1><h1 style="text-align: justify; font-weight: bold;"><span style="font-size:100%;">Ouput: Clocked D Flip-Flop:</span></h1><div style="text-align: justify;">The D flip-flop tries to follow the input D but cannot make the required transitions unless it is enabled by the clock. Note that if the clock is low when a transition in D occurs, the tracking transiton in Q occurs at the next upward transition of the clock.<br /></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq1V5HYGDTitOTjLYljcRyTR1vK2O4X2Pjg5avhVXBj2cWKKmitDCL2PxTXR2BzQp2p6L7kfHTJDKpr4AFScaHaW0hRM6tRlYyveNCngjDorhVVDa0hFNUs3zGC-NxYdGwnEXZoiNEKQ/s1600/Ouput+Clocked+D+Flip-Flop.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 128px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq1V5HYGDTitOTjLYljcRyTR1vK2O4X2Pjg5avhVXBj2cWKKmitDCL2PxTXR2BzQp2p6L7kfHTJDKpr4AFScaHaW0hRM6tRlYyveNCngjDorhVVDa0hFNUs3zGC-NxYdGwnEXZoiNEKQ/s400/Ouput+Clocked+D+Flip-Flop.gif" alt="" id="BLOGGER_PHOTO_ID_5505300628663170450" border="0" /></a><br /></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-89790094666588167322010-08-14T05:03:00.000-07:002010-08-14T05:16:33.363-07:00J-K Flip-Flop<div style="text-align: justify;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1AhyE210HvUhbIvi50fvtTaRNRTJ9kkrFruzf0A7o4gZnPzUNnS3pRcFaAr53Ula4UHe66wC0kYVCMAIkiWh4D1KuiEM5_6uvyeekm5Uekd73YnpTcGpUvyNlQ4A61hyphenhyphenSuK4GI4qfhw/s1600/Block+Diagram+JK+Flick+Flok.gif"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 128px; height: 110px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1AhyE210HvUhbIvi50fvtTaRNRTJ9kkrFruzf0A7o4gZnPzUNnS3pRcFaAr53Ula4UHe66wC0kYVCMAIkiWh4D1KuiEM5_6uvyeekm5Uekd73YnpTcGpUvyNlQ4A61hyphenhyphenSuK4GI4qfhw/s400/Block+Diagram+JK+Flick+Flok.gif" alt="" id="BLOGGER_PHOTO_ID_5505236216040763042" border="0" /></a>The J-K flip-flop is the most versatile of the basic flip-flops. It has the input- following character of the clocked D flip-flop but has two inputs,traditionally labeled J and K. If J and K are different then the output Q takes the value of J at the next clock edge.<img src="file:///C:/DOCUME%7E1/Rashad/LOCALS%7E1/Temp/moz-screenshot.png" alt="" /><img src="file:///C:/DOCUME%7E1/Rashad/LOCALS%7E1/Temp/moz-screenshot-1.png" alt="" /></div><p style="text-align: justify;">If J and K are both low then no change occurs. If J and K are both high at the clock edge then the output will toggle from one state to the other. It can perform the functions of the set/reset flip-flop and has the advantage that there are no ambiguous states. It can also act as a T flip-flop to accomplish toggling action if J and K are tied together. This toggle application finds extensive use in binary counters.<br /></p><h1 style="text-align: left;"><span style="font-size:100%;">J-K Flip-Flop Structure:</span></h1><div style="text-align: justify;">A simplified version of the versatile J-K flip-flop. Note that the outputs feed back to the enabling NAND gates. This is what gives the toggling action when J=K=1.<br /></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguFkoXa9EvHwpWbG9jbSpXK6GKzNNZpXNbCyFQaXRg-5uJBHnu1uW1MwmPU_hsM4-gFHYe9eyvudy2PuRH2zN4uq_uf7syia5vI8DHIdyMpR4vKwJEnLiagEQmUtEyipCrh22qOA8k5g/s1600/Logic+Diagram+JK+Flick+Flok.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 355px; height: 208px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguFkoXa9EvHwpWbG9jbSpXK6GKzNNZpXNbCyFQaXRg-5uJBHnu1uW1MwmPU_hsM4-gFHYe9eyvudy2PuRH2zN4uq_uf7syia5vI8DHIdyMpR4vKwJEnLiagEQmUtEyipCrh22qOA8k5g/s400/Logic+Diagram+JK+Flick+Flok.gif" alt="" id="BLOGGER_PHOTO_ID_5505237768036215394" border="0" /></a><img src="http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/ietron/jk3.gif" /><h1 style="text-align: left;"><br /></h1><h1 style="text-align: left;"><br /></h1><h1 style="text-align: left;"><span style="font-size:100%;">Switching : J-K Flip-Flop:</span></h1><div style="text-align: justify;"><div style="text-align: justify;">The positive going transition (PGT) of the clock enables the switching of the output Q. The "enable" condition does not persist through the entire positive phase of the clock. The J & K inputs alone cannot cause a transition, but their values at the time of the PGT determine the output according to the truth table. This is an application of the versatile J-K flip-flop.<br /><br /></div><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiATyP3vbt7JRbnmzqc9QHqCBTVFAHtsrffj1ntEEWhpKvlaGpuXLCS3cjuuqJjp24UxU2jqhSR7C35TEHMm7bK93pwkeT-WmLXMVyH_Wj3NPb4oy8Zd9YRrZZJNnzy6gvD3hlIX4mI0w/s1600/Switching+Diagram+J-K+Flip-Flop.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 133px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiATyP3vbt7JRbnmzqc9QHqCBTVFAHtsrffj1ntEEWhpKvlaGpuXLCS3cjuuqJjp24UxU2jqhSR7C35TEHMm7bK93pwkeT-WmLXMVyH_Wj3NPb4oy8Zd9YRrZZJNnzy6gvD3hlIX4mI0w/s400/Switching+Diagram+J-K+Flip-Flop.gif" alt="" id="BLOGGER_PHOTO_ID_5505237771646701794" border="0" /></a><br /></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-91010063213114734182010-08-14T04:52:00.000-07:002010-08-14T05:02:35.476-07:00T Flip Flops<span style="font-size:130%;"><span style="font-weight: bold;">T Flip Flops Logic Gate Diagram and Outputs:</span></span><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjC4l5lcJAxLvbmu5SV9LMYhX_cXy9QznTbOcEIEowL4-UJs9urZEjMLAql0kBr_frX11LD_xeH06P1Mhd4jrBj5Yi8SM2r8yJYinfO5im2bX1C4mxe1CFYWbW72G5VUrUNgZnOLjzbyg/s1600/T+Flick+Flok+Ckt.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 400px; height: 213px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjC4l5lcJAxLvbmu5SV9LMYhX_cXy9QznTbOcEIEowL4-UJs9urZEjMLAql0kBr_frX11LD_xeH06P1Mhd4jrBj5Yi8SM2r8yJYinfO5im2bX1C4mxe1CFYWbW72G5VUrUNgZnOLjzbyg/s400/T+Flick+Flok+Ckt.gif" alt="" id="BLOGGER_PHOTO_ID_5505232874719860306" border="0" /></a><br /><br /><div style="text-align: justify;"><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />The T or "toggle" flip-flop changes its output on each clock edge, giving an output which is half the frequency of the signal to the T input.<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZyISnQQa9zG8hRAm1JzPKNfGAYJSaSu7vWLbUD0ldIenabHN5qxd_WjIo6GCwBtlcQp8-EkHBotkEWtRsFfDSv3wI7rgQyTBazK-_dETwOkKcVfyPqjdKFhHjiX-B8Uu9eOv4jtH_1A/s1600/T+Flick+Flok+sig.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 363px; height: 89px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZyISnQQa9zG8hRAm1JzPKNfGAYJSaSu7vWLbUD0ldIenabHN5qxd_WjIo6GCwBtlcQp8-EkHBotkEWtRsFfDSv3wI7rgQyTBazK-_dETwOkKcVfyPqjdKFhHjiX-B8Uu9eOv4jtH_1A/s400/T+Flick+Flok+sig.gif" alt="" id="BLOGGER_PHOTO_ID_5505232890074493522" border="0" /></a><br /><br /><br /><br /><br /><br /><br />It is useful for constructing binary counters, frequency dividers, and general binary addition devices. It can be made from a J-K flip-flop by tying both of its inputs high.</div><br />Construction of T flip-flop from a J-K flip-flop.<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1GRMYtuvUfso3OTtaIZpNdRLcSqq4eFsnXI7eA27we46mx6iIL0TBjAKelNmKN21yv6Z9eeArrVlPYaWGoGtTk2N-4mlginAl_M-9JU6oStdh4f-JCfgSQvEgl31U0DUQTy8Pve2Tog/s1600/T+Flick+Flok+jk.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 200px; height: 95px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1GRMYtuvUfso3OTtaIZpNdRLcSqq4eFsnXI7eA27we46mx6iIL0TBjAKelNmKN21yv6Z9eeArrVlPYaWGoGtTk2N-4mlginAl_M-9JU6oStdh4f-JCfgSQvEgl31U0DUQTy8Pve2Tog/s400/T+Flick+Flok+jk.gif" alt="" id="BLOGGER_PHOTO_ID_5505232882812150786" border="0" /></a>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-66421176838527910.post-25456307497464680302010-08-14T04:37:00.000-07:002010-08-14T04:45:59.589-07:00Binary Counting<div style="text-align: justify;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVOh5PLzRbXQ1MP3QfHLjXS_-B4W9B89-z399Huop7OrHcYF2pb5OI9a1QQMl0bGCKsnu14x7vTKcpRZCIE3aUUIdmDsIArCZvLyP9saL0yVUm6xYXWLkbfsAGh8reV7DBdf4N_w21bQ/s1600/bincount.gif"><img style="margin: 0pt 0pt 10px 10px; float: right; cursor: pointer; width: 291px; height: 327px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVOh5PLzRbXQ1MP3QfHLjXS_-B4W9B89-z399Huop7OrHcYF2pb5OI9a1QQMl0bGCKsnu14x7vTKcpRZCIE3aUUIdmDsIArCZvLyP9saL0yVUm6xYXWLkbfsAGh8reV7DBdf4N_w21bQ/s400/bincount.gif" alt="" id="BLOGGER_PHOTO_ID_5505230356615528850" border="0" /></a>A binary counter can be constructed from J-K flip-flops by taking the output of one cell to the clock input of the next. The J and K inputs of each flip-flop are set to 1 to produce a toggle at each cycle of the clock input. For each two toggles of the first cell, a toggle is produced in the second cell, and so on down to the fourth cell. This produces a binary number equal to the number of cycles of the input clock signal. This device is sometimes called a "ripple through" counter.</div>Unknownnoreply@blogger.com0