Design problem: How do you detect if two 8-bit numbers/signals are equal

Here, the problem involves detecting if each bit of a signal is equal to corresponding bit of the other signal and then generating a resultant. First of all, the circuit which provides equivalence of 1-bit is nothing but an XNOR gate as explained here. So, we require 8 XNOR gates to judge equivalence of individual bits. Even if one of the bits is "0", it means the numbers are not equal, which can be obtained by ANDing the eight bits together.

Alternatively, we can use an XOR gate as well. An XOR gate provides output as "1" if the two inputs are not equal as explained here. Even if one of the 8 individual XOR gates provides output as "1", it will mean that the numbers are not equal, which can be obtained by NORing the eight bits together.

Can you judge which of these can be implemented with less area and power?

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