Design a two-bit comparator from two 1-bit comparators as the building blocks. Note: Problem 1 might be helpful in solving this one. Assume you have access to two of these 1-bit comparators that we have built in lecture. Namely, comparators C0 and C1. You are given two 2-bit binary numbers X and Y. X is composed of bits x1 and x0 and Y is composed of bits y1 and y0. Bit subscripts corresponds to the significance i.e. x1 is the MSB of X and x0 is the LSB of X and the same goes for Y. Each Comparator outputs are labeled as follows:EQ0 (i.e. y0 = x0), YGX0 (i.e. y0 > x0), and XGY0 (i.e. y0 <>
EQ1 (i.e. y1 = x1), YGX1 (i.e. y1 > x1), and XGY1 (i.e. y1 <>
The Comparator to be designed is called “C”.
The outputs of that Comparator are:
EQ (i.e. Y = X), YGX (i.e. Y > X), and XGY (i.e. Y
Your task is to derive an expression for the three outputs of the 2-bit comparator that you are designing.
Namely, Express EQ, XGY, YGX as functions of EQ0, YGX0, XGY0, EQ1, YGX1, and XGY1 and not as functions of x0, y0, x1, nor y1.