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phase/decomposing_boolean_algebra.txt

Created August 27, 2016 01:02
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Decomposing Boolean Algebra
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decomposing_boolean_algebra.txt
Not(a) = Nand(a,a)
And(a,b) = Not(Nand(a,b))
Or(a,b) = Not(And(Not(a),Not(b)))
Xor(a,b) = Or(And(a,Not(b)),And(Not(a),b)))
Or(a, b) =
Nand( //Not
Nand( //And
Nand(Nand(a, a), Nand(b, b)), //First And input
Nand(Nand(a, a), Nand(b, b)) //Second And input
),
Nand( // Copy of above for the Not
Nand(Nand(a, a), Nand(b, b)),
Nand(Nand(a, a), Nand(b, b))
)
)
Or(a, b) = Nand(Nand(Nand(Nand(a, a), Nand(b, b)), Nand(Nand(a, a), Nand(b, b))), Nand(Nand(Nand(a, a), Nand(b, b)), Nand(Nand(a, a), Nand(b, b))))
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