Tool to calculate the dual of a Boolean logical expression. The dual being a complementary expression inverting addition and multiplication as well as 0 and 1.

Boolean Dual - dCode

Tag(s) : Symbolic Computation, Electronics

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The dual of a Boolean or of a Boolean expression is obtained by applying 2 operations: replacing/interchanging the logical ORs by logical ANDs and vice versa and replacing/interchanging the logical 0s by logical 1s and vice versa.

__Example:__ The dual of `a+b` is `a.b` and conversely the dual of `a.b` is `a+b` (duality principle)

It is possible that the value $ a $ itself has a dual, some note this dual $ a' $ (be careful not to confuse this notation with the boolean NOT unary operator)

The dual of a boolean function $ F $ is sometimes denoted by $ Fˊ $ (not to be confused with the complement or NOT function) or $ F ^ d $.

Likewise `0` and `1` are dual, `true` and `false` are duals, `∧` and `∨` are dual.

Every Boolean expression has a dual, the Boolean Duality principle means that every theorem or any computation has a dual equivalent.

By proving something in Boolean algebra, its dual is also proved.

__Example:__ `x+1=1` has for dual `x.0=0`

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*Boolean Dual* on dCode.fr [online website], retrieved on 2024-07-15,

dual,duality,boolean,boole,logic

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