Simplification using Boolean algebra
Let us consider an example of a Boolean function: AB+A (B+C) + B (B+C)
The logic diagram for the Boolean function AB+A (B+C) + B (B+C) can be represented as:
We will simplify this Boolean function on the basis of rules given by Boolean algebra.
AB + A (B+C) + B (B+C)
AB + AB + AC + BB + BC {Distributive law; A (B+C) = AB+AC, B (B+C) = BB+BC}
AB + AB + AC + B + BC {Idempotent law; BB = B}
AB + AC + B + BC {Idempotent law; AB+AB = AB}
AB + AC +B {Absorption law; B+BC = B}
B + AC {Absorption law; AB+B = B}
Hence, the simplified Boolean function will be B + AC.
The logic diagram for Boolean function B + AC can be represented as:
