Question

Simplify the Boolean expression [AB(C + B'D') + A'B']CD.

Answer 1

The simplified Boolean expression is CD, achieved by applying Boolean algebra properties such as the distributive law, complement, and identity laws.

Step-by-step explanation:

The student has presented a Boolean algebra expression that needs to be simplified. To do this, we apply various properties of Boolean algebra including the commutative, distributive, and identity laws. The goal is to eliminate terms wherever possible to achieve the simplest form of the expression.

Let's simplify the expression step by step:

1. Expand the expression using the distributive law: AB(C + B'D') + A'B'CD
2. Notice that AB'B' = 0 because B'B' = B' (self-identity) and AB' = 0 (complement).
3. Also, note that ABB'D' = 0 because BB' = 0 (complement).
4. Apply these simplifications: ABC + ABD' + A'B'CD = ABC + A'B'CD (since ABD' = 0).
5. Factor out CD: (AB + A'B')CD.
6. Apply the identity law: (A + A') = 1, so (AB + A'B') = B + B' = 1 (complement).
7. Thus, the expression simplifies to CD, as (1)CD = CD.

Therefore, the simplified Boolean expression is CD.