Answer to Question #163525 in Electric Circuits for Aarati

Question

Design and implement a 1-bit comparator using logic gates.

Answer 1

A 1-bit comparator compares two single bits.

Let’s apply a shortcut to find the equations for each of the cases. Normally, we can use a K-map. But this shortcut is efficient and handy when you understand it.

For A>B, there is only one case when the output is high when A=1 and B=0. Let’s call this X. We can write the equation as follows

X(which stands for A>B) = AB’

Similarly, denote A<B with Y and A=B with Z.

Y = A’B

Since Z is high in two cases, there will be an OR gate. This is because the logic behind an OR gate is that a high output can be achieved in one or more cases. Z is high when A=0 and B=0, it is also high when A=1 and B=1. Therefore,

Z = A’B’ + AB

This is similar to the equation of an EXNOR gate. Hence,

$Z=A \oplus B$