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Boolean Algebra
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If input A is 0 then A' will be 1, and if A is 1 then NOT A will be 0 - they cannot both be 1!
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B
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A
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X.Z + X.Y + W.Z; alternatively: X.(Z + Y) + W.Z
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A + B
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A.B'
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A.B
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A.B' + A'.B (A XOR B)
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A.B (A AND B)
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A.B' + C
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A'.B + A.B' (A XOR B)
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A.C'
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A + B (A OR B)
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A
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