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

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

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

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

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

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)’