What is the minimum number of 2-input NOR gates that are required for implementing a 2-input XNOR function?

To implement a 2-input XNOR function using NOR gates, we can follow these steps:

Step 1: Understand the XNOR function The XNOR function returns true (1) if both inputs are the same, and false (0) otherwise. The truth table for a 2-input XNOR function is as follows:

Step 2: Determine the logic expression for XNOR From the truth table, we can derive the logic expression for the XNOR function as follows:

XNOR = (A AND B) OR (NOT A AND NOT B)

Step 3: Implement the XNOR function using NOR gates To implement the XNOR function using NOR gates, we can use De Morgan's theorem, which states that the complement of a logical expression can be obtained by inverting the inputs and outputs of the gates and changing the gate type.

Using De Morgan's theorem, we can rewrite the XNOR expression as:

XNOR = NOT (A OR B) OR (A AND B)

Step 4: Determine the number of NOR gates required From the rewritten expression, we can see that we need one NOR gate for the A OR B operation and one NOR gate for the A AND B operation.

Therefore, the minimum number of 2-input NOR gates required for implementing a 2-input XNOR function is 2.