Encoder

An encoder is a digital function that produces a reverse operation from that of a decoder. An encoder has 2ⁿ(or less) input lines and n output lines. The output lines generate the binary code for the 2ⁿ input variables.

We found from truth table x=D4+D5+D6+D7; y=D2+D3+D6+D7; z=D1+D3+D5+D7

D₀ is not connected to any OR gate; the binary output must be all 0’s in this case.

The ckt has 8 inputs and could have 2⁸=256 possible input combinations. Only 8 of these combinations have any meaning. The other inputs combinations are don’t care conditions.