Question

Find f(A,B,C,D) by simplifying the following expression using Boolean algebra:

f(A,B,C,D)​=A+A⋅B⋅Dˉ+A⋅Bˉ⋅C

Answer 1

The simplified expression is A + A⋅B⋅Dˉ+A⋅Bˉ⋅C.

Step-by-step explanation:

The expression can be simplified using the distributive property, De Morgan's Laws, the identity laws, the null laws, the idempotent laws, and the absorption laws.

Steps to simplify the expression:

Distribute the AND operator over the OR operator:

f(A,B,C,D) = A + (A⋅B⋅Dˉ) + (A⋅Bˉ⋅C)

Apply the distributive property:

f(A,B,C,D) = A + (A⋅B⋅Dˉ) + (A⋅Bˉ⋅C) = (A * B * Dˉ) + (A * Bˉ * C) + A

Apply De Morgan's Laws:

f(A,B,C,D) = (A * B * Dˉ) + (A * Bˉ * C) + A = (A * B * Dˉ) + (A * (¬B + C)) + A

Apply the identity laws:

f(A,B,C,D) = (A * B * Dˉ) + (A * (¬B + C)) + A = (A * B * Dˉ) + (A * C) + A

Apply the null laws:

f(A,B,C,D) = (A * B * Dˉ) + (A * C) + A = (A * B * Dˉ) + (A * C) + 1A

Apply the idempotent laws:

f(A,B,C,D) = (A * B * Dˉ) + (A * C) + 1A = A(B * Dˉ) + A(C) + A

Apply the absorption laws:

f(A,B,C,D) = A(B * Dˉ) + A(C) + A = A + A(C) + A = A + A(C)

Therefore, the simplified expression is A + A⋅B⋅Dˉ+A⋅Bˉ⋅C.