Introduction to DLD

XOR Gate Using NOR Gates

An XOR 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, OR, AND, NOR, XOR, and XNOR. Implementing an XOR gate using a NOR gate is useful when you need an XOR logic circuit but only have NOR gates available; an XOR logic gate is not available.

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

XOR Logic Gate

XOR (Exclusive-OR) gate is a digital logic gate that produces HIGH (1) output when its inputs are different. When the inputs are the same, the output is LOW (0).

For a 2-input XOR gate:

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

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

XOR Gate Using NOR Gate - XOR 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 HIGH (1) output only when all inputs are LOW (0). If any input is HIGH (1), the output becomes LOW (0).

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

XOR Gate Using NOR Gate - NOR Logic Gate (2 Inputs)

 

XOR Gate Using NOR Gates

If we want to construct a 2-input XOR logic gate using NOR gates, then 5 NOR gates are required to implement this process. The following diagram explains the entire process.

XOR Gate Using NOR Gate

Let’s explain the above diagram in 5 simple steps

STEP 01 – XOR 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

XOR Gate Using NOR Gate - Step 1

STEP 02 – XOR 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

XOR Gate Using NOR Gate - Step 2

STEP 03 – XOR 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

XOR Gate Using NOR Gate - Step 3

STEP 04 – XOR Gate Using NOR Gate

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

XOR Gate Using NOR Gate - Step 4

STEP 05 – XOR Gate Using NOR Gate

NOR Gate 5: Takes (A’B + AB’)’ as both inputs and produces the final output A ⊕ B. The following diagram explains the working of the 5th (last)     NOR logic gate

XOR Gate Using NOR Gate - Step 5