Answer to Question #290629 in Discrete Mathematics for Yaku

Question

Suppose that, in the circuit for a 2-bit comparator, we wanted to allow for inputs from the

higher byte comparisons, xH < yH, xH = yH, xH > yH, so that we could now use a 2-bit

comparator in cascades for building comparators for numbers with more than 2 bits.

a) Re-write the equations for a 2-bit comparator that would allow for the inputs: xH < yH,

xH = yH, xH > yH.

b) Re-draw the corresponding circuit diagram.

Answer 1

a) xH < yH = xH₁^_ xH₀^_ yH + xH₁ yH + xH₀ yH₁yH₀

 xH =yH = (xH₀ E_x-NOR yH₀ ) ( xH₁ E_X-NOR yH₁ )

xH > yH. = xH₀ yH₁^_ yH_{0 +} xH₁ xH₀yH₀^_ + xH₁ yH₁^_

b).