Introduction to DLD

XNOR Gate Using NOR Gate

An XNOR logic Gate can be made using NOR logic gates. As we know, NOR is a universal logic gate, meaning it can be used to build other basic logic gates such as NOT, AND, OR, NOR, XOR, and XNOR. Implementing an XNOR gate using a NOR gate is useful when you need an XNOR logic circuit but only have NOR gates available; an XNOR logic gate is not available.

XNOR Gate Using NOR Gate - Need to Produce XNOR Gate Result

 

XNOR Logic Gate

XNOR (Exclusive-NOR) gate is a digital logic gate that produces LOW (0) output when its inputs are different. When the inputs are the same, the output is HIGH (1).

For a 2-input XNOR gate:

  • Output is 0 when one input is 1 and the other is 0.
  • Output is 1 when both inputs are 0 or both are 1.

The XNOR logic gate truth table and its symbol are given below.

XNOR Gate Using NOR Gate - XNOR Logic Gate Truth Table (2-Inputs)

NOR Logic Gate

A NOR logic gate is a combination of an OR gate and a NOT gate. It produces a HIGH (1) output only when all inputs are LOW (0). If any input is HIGH (1), the output is LOW (0).

The basic NOR logic gate with its truth table is given below

XNOR Gate Using NOR Gate - NOR Logic Gate 2 inputs

XNOR Gate Using NOR Gates

If we want to construct a 2-input XNOR logic gate using NOR gates, then 4 NOR gates are required to implement this process. The following diagram explains the entire process.

XNOR Gate Using NOR Gate - Final Implementation

Let’s explain the above diagram in 4 simple steps

STEP 01 – XNOR Gate Using NOR Gate

NOR Gate 1: Takes inputs A and B and produces (A + B)’. The following diagram explains the working of the first NOR logic gate

XNOR Gate Using NOR Gate - STEP 1

STEP 02 – XNOR Gate Using NOR Gate

NOR Gate 2: Takes inputs A and (A + B)’ and produces A’B. The following diagram explains the working of the second (top) NOR logic gate

XNOR Gate Using NOR Gate - STEP 2

STEP 03 – XNOR Gate Using NOR Gate

NOR Gate 3: Takes inputs B and (A + B)’ and produces  AB’. The following diagram explains the working of the third (bottom) NOR logic gate

XNOR Gate Using NOR Gate - STEP 3

STEP 04 – XNOR Gate Using NOR Gate

NOR Gate 4: Takes inputs A’B and AB and produces (A’B + AB’)’ which is the required result (A ⊕ B)’. The following diagram explains the working of the 4th (second to last) NOR logic gate

XNOR Gate Using NOR Gate - STEP 4

 

XNOR Gate Using NOR Gate – Truth Table

The following truth table shows the XNOR gate using NOR gates. The final output is 1 when both inputs are the same and 0 when the inputs are different.

XNOR Gate Using NOR Gate - XNOR Logic Gate Truth Table (2-Inputs) final