Simplifying Boolean expressions

• Example 2: A full adder's carry-out function  Cout = A'BCin + AB'Cin + ABCin' + ABCin = A'BCin + AB'Cin + ABCin' + ABCin + ABCin = A'BCin + ABCin + AB'Cin + ABCin' + ABCin = (A'+A)BCin + AB'Cin + ABCin' + ABCin = (1)BCin + AB'Cin + ABCin' + ABCin = BCin + AB'Cin + ABCin' + ABCin + ABCin = BCin + AB'Cin + ABCin + ABCin' + ABCin = BCin + A(B'+B)Cin + ABCin' + ABCin = BCin + A(1)Cin + ABCin' + ABCin = BCin + ACin + AB(Cin'+Cin) = BCin + ACin + AB(1) = BCin + ACin + AB

associative

idempotent

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