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What is a Universal Gate and Why NOR is called a Universal gate?

Posted by Nityanand Dubey on December 4, 2009

This is a continuation of previous post, in this post, we will see the NOR gate as a univarsal gate and create different gates using NOR gate.

As we know that NAND and NOR Gates are called Universal Gates since they can cerate any of the Logic Gate

Lets see to how to make all other logic gates by using the NOR Gate

1. NOR gate to NOT Gate conversion

Refer the following diagram –

Digital : Image – NOR to NOT

NOR to NOT Conversion

NOR to NOT Conversion

Here the same input is applied to the both inputs of a NOR Gate

According to NOR Gate – If A and B are two inputs than output equation will be (A+B)’

For this case :

= (X+X)’
= X’
= Inverted Input

2. NOR Gate to AND Gate Convertion

Refer following diagram for NOR to AND Gate conversion -

Digital : Image – NOR to AND Conversion

NOR to AND Conversion

NOR to AND Conversion

According to diagram –

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

3. NOR Gate to OR Gate Convertion

Refer the following Diagram

Digital : Image – NOR to OR Convertion

NOR to OR

NOR to OR


For this case – X and Y are the two inputs to a NOR gate and the output of the First NOR gate goes again to an another NOR gate’s inputs.

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

=> OR Gate

4. NOR Gate to NAND Gate Convertion

Refer the following Diagram

Digital : Image – NOR to NAND

NOR to NAND Conversion

NOR to NAND 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)’
=> NAND Gate

5. NOR to XOR Gate

Digital : Image – NOR to XOR Gate Convertion

6. NOR to XNOR Gate

Digital : Image – NOR to XNOR Gate Convertion

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2 Responses to “What is a Universal Gate and Why NOR is called a Universal gate?”

  1. ANU roy said

    like

  2. Zohaib said

    great job man……….. very well done……………………. and thanks for such a nice post

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