Magnitude Comparator

A magnitude comparator is a combinational ckt that compares two numbers, A and B, and determines their relative magnitudes.

The outcomes of the comparison is specified by three binary variables that indicate whether A>B, A=B or A

Consider two numbers A and B, with four digits each A=A₃A₂A₁A₀ and B=B₃B₂B₁B₀

The equivalence function: xi=AiBi+A’iB’i as i=0,1,2,3,….

If (A=B)=x₃x₂x₁x₀

(A>B)=A₃B’₃+x₃A₂B’₂+x₃x₂A₁B’₁+x₃x₂x₁A₀B’₀

(A₃B₃+x₃A’₂B₂+x₃x₂A’₁B₁+x₃x₂x₁A’₀B₀