What is the minimum number of 2-input NOR gates that are required for implementing a 2-input XNOR function?2543

To implement a 2-input XNOR function, we can use a combination of NOR gates.

Step 1: Start by understanding the truth table of a 2-input XNOR gate. The XNOR gate outputs a high (1) only when both inputs are the same (either both 0 or both 1).

Inputs (A, B) | Output (XNOR)

0, 0 | 1 0, 1 | 0 1, 0 | 0 1, 1 | 1

Step 2: Based on the truth table, we can see that the XNOR function can be expressed as the negation of the XOR function. Therefore, we can implement the XNOR function using a combination of NOR gates.

Step 3: The XOR function can be implemented using three NOR gates. The XOR gate outputs a high (1) only when the inputs are different.

Inputs (A, B) | Output (XOR)

0, 0 | 0 0, 1 | 1 1, 0 | 1 1, 1 | 0

Step 4: To obtain the XNOR function, we can simply negate the output of the XOR gate using another NOR gate.

Step 5: Therefore, the minimum number of 2-input NOR gates required for implementing a 2-input XNOR function is four. Three NOR gates for implementing the XOR function and one additional NOR gate for negating the XOR output.