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NOR Gate as a Universal Gate

Updated: Mar 5


NOR Gate as Universal Gate

You might have already seen the basic #logicgates before arriving at this article. #NOR gate has a special property amongst the gates. It allows users to design any logical Boolean expression using NOR gates alone if composed properly. This property is practiced to #NAND gates also.


A NOR is nothing but a gate that gives an inverted output of the OR gate. Let us take a short peek at the gate and its #truthtable.


Nor Gate

Input A Input B Output Q


  0 0 1

0 1 0

1 0 0

1 1 0


So how does this implementation actually work? Dive in right away.


NOT using NOR gate


This can be made by simply joining the two inputs of the NOR gate. Because a NOR gate is similar to an OR gate that leads to NOT gate, this immediately removes the "OR" part of the NOR gate, removing it from consideration and keeping just the NOT part.


NOT Gate




The desired output of the NOT gate is Q = NOT( A ).


Not Gate






The implementation of the NOT gate using the NOR gate is A NOR A.


OR gate using NOR gate


The NOR gate is the inverted #circuit of an OR gate. So if we invert the NOR gate again, there it is, back to the OR gate. Check out the implementation for more clarity.


OR Gate




The expected output of the OR gate is Q = A OR B.




OR Gate




The implementation of the OR gate using NOR gates is { A NOR B } NOR { A NOR B }.



AND gate using NOR gate


The output of the AND gate is TRUE only if both the inputs are TRUE. So, AND is implemented by inverting the inputs of the NOR gate.


AND Gate






The desired output of the AND gate is Q = A AND B.


And Gate








The actual implementation of AND gates using NOR gates is { A NOR A } NOR { B NOR B }.


NAND gate using NOR gate


We already saw how to implement AND using NOR gates. NAND is the inversion of AND gate and can be implemented by adding another NOR gate to reverse the output. Sounds pretty easy right?


NAND Gate





The desired implementation of the NAND gate is Q = A NAND B.


NAND Gate







The actual implementation of the NAND gate using NOR gates is [ ( A NOR A ) NOR ( B NOR B ) ] NOR [ ( A NOR A ) NOR ( B NOR B ) ].


XNOR using NOR gates


#XNOR gate can be implemented using NOR gates in two ways; one using 4 gates and other using 5 gates.


XNOR Gate







The desired implementation of the XNOR gate Q = A XNOR B.

First, let us take a look at the implementation that is most commonly used.


XNOR Gate






Here the output will be: -

{ B NOR ( A NOR B ) } NOR { A NOR ( A NOR B ) } .


There is also a conjunctive normal form that is often used. This is derived from DeMorgan's law and requires 5 nor gates for the implementation.


NOR Gate







Here the output will be: -

{ A NOR ( B NOR B ) } NOR{ B NOR ( A NOR A ) }.


XOR using NOR gates



XOR gate gives a TRUE output when an odd number of inputs are TRUE. This circuit can also be in two ways.


Xor Gate







The desired output of the XOR gate is Q = A XOR B.


The first implementation of XOR requires the use of 5 NOR gates.


XOR Gate







The output of the implementation is as: -

{ ( A NOR A ) NOR ( B NOR B ) } NOR ( A NOR B )


There is also a version of XOR using NOR gates that is often used as it has a cleaner circuit.

It is done by adding an inverter to an XNOR implementation using 4 gates.


XNOR Gate





{ A NOR ( A NOR B ) ] NOR



[ B NOR ( A NOR B ) ] } NOR

{ [ A NOR ( A NOR B ) ]

NOR [ B NOR ( A NOR B ) }


Hence we understand that any boolean circuit can be implemented using NOR gates alone. Try doing some of the #booleanexpressions by yourself using these implementations.

DRAFTJS_BLOCK_KEY:27f38You might have already seen the basic



 

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2 Comments


Anushka Gupta
Anushka Gupta
Jul 31, 2023

Thanks to Learn Electronics India's exceptional blog, I'm inspired to experiment and explore the power of NOR gates in my electronics projects. The real-world examples and practical tips shared in the article make it an invaluable resource for anyone interested in digital electronics. I'm grateful for stumbling upon this gem.

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LearnElectronics India simplifies complex concepts beautifully. Thank you!

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