Universal Logic Gates – NAND Gate and NOR Gate

A universal logic gate is a type of logic gate that can be used to implement any logical function without any other type of logic gate. 

There are two types of universal logic gates: NAND gate and NOR gate.

These are called universal logic gates because they can perform all three basic logic operations, i.e. AND, OR, and NOT.  Let us explore how these 2 universal logic gates work –

• NAND Universal Logic Gate
  • AND Gate Using NAND Gate
  • OR Gate Using NAND Gate
  • NOR Gate Using NAND Gate
  • XNOR Gate Using NAND Gate
  • XOR Gate Using NAND Gate
• NOR Universal Logic Gate
  • AND Gate Using NOR Gate
  • OR Gate Using NOR Gate
  • NAND Gate Using NOR Gate
  • XNOR Gate using NOR Gate
  • XOR Gate Using NOR Gate

NAND Universal Logic Gate

The NAND is a universal gate. It can be used to create any other type of logic gate. Here are the techniques for implementing fundamental gates using NAND gates:

AND Gate Using NAND Gate

You require two NAND gates to create an AND gate. 

• In the first NAND gate, the outcome is the inverse of the logical AND operation between the two inputs. 
• The second NAND gate then inverts the output from the first gate, thus producing the original AND logic.

A NAND gate is employed as an AND gate by inverting its inputs and output. The outcome replicates the behavior of an AND gate, where only when both inputs are 1 does the output become 0 due to the inversion.

OR Gate Using NAND Gate

Constructing an OR gate involves three NAND gates. 

• The first NAND gate produces the inverse of the first input.
• The second NAND gate generates the inverse of the second input.
• The third NAND gate computes the logical OR of the outputs from the first two NAND gates.

A NAND gate is used as an OR gate by inverting its inputs and output. The result is that when both inputs are 0, the NAND gate outputs 1, simulating an OR gate’s behaviour.

NOR Gate Using NAND Gate

A NOR gate with inputs A and B can be constructed using three NAND gates as follows:

First NAND Gate

• Connect inputs A and B to the two inputs of the first NAND gate.
• The output of the first NAND gate will be A NAND B (A.B) since NAND is the complement of AND.

Second NAND Gate

• Connect the output of the first NAND gate (A.B) to both inputs of the second NAND gate.
• The output of the second NAND gate will be the complement of A.B, which is ¬(A.B).

Third NAND Gate

• Connect the outputs of the first and second NAND gates to the two inputs of the third NAND gate.
• The output of the third NAND gate will be ¬(A.B) NAND ¬(A.B), which simplifies to ¬(A.B).

An XNOR gate can be implemented using NAND gates –

XNOR Gate Using NAND Gate

• The first NAND gate takes the inputs A and B and inverts them. 
• The second NAND gate takes the inverted inputs and performs an OR operation. 
• The third NAND gate takes the output of the second NAND gate and inverts it again. 

The output of the third NAND gate is the output of the XNOR gate.

XOR Gate Using NAND Gate

Building an XOR gate requires four NAND gates. 

• The first two NAND gates produce the inverse of the respective inputs. 
• The third NAND gate computes the logical AND of the outputs from the first two NAND gates. 
• The fourth NAND gate inverts the output of the third NAND gate, resulting in the XOR operation.

NOR Universal Logic Gate

The NOR gate is also universal and can be used to create any other kind of logic gate. Below are the methodologies for implementing fundamental gates using NOR gates:

AND Gate Using NOR Gate

Three NOR gates are required to construct an AND gate. 

• The first NOR gate’s output is the inverse of the logical OR operation between the two inputs. 
• The second NOR gate inverts the output of the first NOR gate, resulting in the original AND logic.

OR Gate Using NOR Gate

An OR gate can be created using two NOR gates, as demonstrated. 

• The output of the first NOR gate is the complement of each input. 
• The second NOR gate computes the logical OR of the outputs from the first NOR gate.

NAND Gate Using NOR Gate

A NAND gate can be implemented using NOR gates. 

1. The first NOR gate takes the input A and inverts it. 
2. The second NOR gate takes the input B and inverts it. 
3. The third NOR gate takes the outputs of the first two NOR gates and performs an OR operation. 
4. The output of the third NOR gate is the output of the NAND gate.

XNOR Gate using NOR Gate

• The first NOR gate takes the inputs A and B and inverts them. 
• The second NOR gate takes the inverted inputs and performs an OR operation. 
• The third NOR gate takes the output of the second NOR gate and inverts it again. 

The output of the third NOR gate is the output of the XNOR gate.

XOR Gate Using NOR Gate

An XOR gate can be implemented using 3 NOR gates –

• The 1st NOR gate takes the inputs A and B and inverts them. 
• The 2nd NOR gate takes the inverted inputs and inverts them again. 
• The 3rd NOR gate takes the outputs of the first two NOR gates and performs a NOR operation. 

The output of the third NOR gate is the output of the XOR gate.

We hope this blog helped you understand how universal logic gates, NAND and NOR work.