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What is a Universal Gate and Why NAND is called a Universal gate?

Posted by Nityanand Dubey on March 6, 2009

A Logic Gate which can infer any of the gate among Logic Gates. OR a gate which can be use to create any Logic gate is called Universal Gate

We have following Logic Gates

NOT
AND
OR
NAND
NOR
XOR
XNOR

NAND and NOR Gates are called Universal Gates because all the other gates can be created by using these gates

In this post, we will see to how to make all other logic gates by using the NAND Gate

1. NAND gate to NOT Gate conversion

Refer the following diagram –

Digital : Image – NAND to NOT

Nand to Not conversion

Nand to Not conversion

Here the same input is applied to the both inputs of a NAND Gate

According to NAND Gate – If A and B are two inputs than output equation will be (A.B)’

For this case :

= (X.X)’
= X’

2. NAND Gate to AND Gate Convertion

Refer following diagram for NAND to and Gate conversion -

Digital : Image – NAND to AND

NAND to AND conversion

NAND to AND conversion

For this case – x and y are the two inputs to a NAND gate and the output of the First NAND gate goes again to an another NAND gate’s inputs.

=> s1 = (X.Y)’
=> s2 = (s1.s1)’ = s1’
=> s2 = ((X.Y)’)’
=> X.Y

3. NAND Gate to OR Gate Conversion

Refer the following Diagram

Digital : Image – NAND to OR

NAND to OR Conversion

NAND to OR Conversion

According to diagram –

s1 = (X.X)’ = X’
s2 = (Y.Y)’ = Y’
s3= (s1.s2)’ = (X’.Y’)’
=> (X’)’ + (Y’)’
=> X+Y

4. NAND Gate to NOR Gate Convertion

Refer the following Diagram

Digital : Image – NAND to NOR

NAND to NOR conversion

NAND to NOR conversion

According to diagram –

s1 = (X.X)’ = X’
s2 = (Y.Y)’ = Y’
s3= (s1.s2)’ = (X’.Y’)’
=> (X’)’ + (Y’)’
=> X+Y
s4 = (s3.s3)’ = s3’
=> (X + Y)’

5. NAND to XOR Gate

Digital : Image – 5

6. NAND to XNOR Gate

Digital : Image – 6



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