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 using the rules of 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 {Absorption law; B+BC = B}
B + AC {Absorption law; AB+B = B}
Therefore, the simplified Boolean function is \ (B + AC \).
The logic diagram for the Boolean function \(B + AC \) can be represented as follows:
