Electronic – How to implement a function using just NAND or NOR logic gates

digital-logiclogic-gates

I am trying to understand the process of creating combinatorial circuits. I understand that first we document the inputs and outputs, then create minterms and max terms, then push them into a k-map and get a function as an output. This function can then be implemented using logic gates.

The problem I have is, I don't understand the logic behind converting the equation that we got, such that I can implement the same circuit using just NAND or nor logic gates.

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The image is from my book for converting a half adder circuit. I understand the steps taken but don't understand the reason why they took them. Thanks for the help.

Best Answer

Start with your equation as normal...
Y = ABC+DEF+GHI+JKL...

Repeatedly apply de'Morgan's Theorem to convert all AND and OR and NOT operations into either NAND or NOR as required.

AND(A,B,C,D...) = NAND(NOT(A),NOT(B),NOT(C),NOT(D)...)

OR(A,B,C,D...) = NOR(NOT(A),NOT(B),NOT(C),NOT(D)...)

NOT(A) = NOR(A,0)

NOT(A) = NOR(A,A)

NOT(A) = NAND(A,1)

NOT(A) = NAND(A,A)


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