Question

Using the theorems of Boolean algebra, minimize the following logical expressions. Express the answer as a sum of multiple product terms.

Answer 1

The task is to use Boolean algebra theorems to minimize logical expressions, aiming to express the results as a sum of product terms which leads to efficient digital circuit designs.

Step-by-step explanation:

The question involves using Boolean algebra theorems to minimize logical expressions. Minimization involves applying various laws such as the identity law, the null law, the idempotent law, the complement law, the associative law, the distributive law, and DeMorgan's Theorems. The goal is to simplify the expression into its simplest form, ideally with a sum of products format. A minimized Boolean expression results in a more efficient digital circuit design.

To minimize an expression, you typically follow these steps:

1. Identify and apply simplification theorems to reduce the number of terms and literals.
2. Simplify the expression by combining like terms and eliminating redundancies.
3. After simplification, double-check it against the original expression to ensure its accuracy and that it adheres to the constraints of Boolean algebra.

In the given problem, without the specific logical expression, we cannot provide a step-by-step process. However, students should use the theorems mentioned above. After simplification, they must verify that the output of the minimized expression matches the output of the original expression for all possible inputs to ensure its reasonableness.