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How can I form a complete operator base from XOR and AND?

a and b = a and b

a or b = (a xor b) xor (a and b)

but I can't find a solution for NOT

Thanks for your help
in # Mandatory Modules Bachelor by (130 points)

1 Answer

+3 votes

¬a = a ⊕ 1  

Using other notation,  not a = a xor 1

by (2.5k points)
And the 1 is needed as a constant since you cannot express not with {and, xor} alone. That is why the Reed-Muller form has the additional xor with 1 to express negation.

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