Single-bit magnitude comparator

A single-bit magnitude comparator compares between two single-bit values. There can be 4 possible cases for two single bit values A and B as follows:

• A = B
• A > B
• A < B
• A != B

The truth table showing each of the cases is shown in figure below:

Let us use K-maps for deriving the logic for each of the four outputs as shown in figure below.

Thus, we get

Equation of (A = B) : A (xnor) B

Equation of (A < B) : A' B

 Equation of (A > B) : A B'

Equation of (A != B) : A (xor) B