Simplification using Boolean algebraLet 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: Next TopicMap Simplification |