Converting W(X + YZ) to standard SOP form By applying which Boolean algebra law can the expression W(X + YZ) be expanded into a sum-of-products (SOP) form?

Introduction / Context:In digital logic design, we frequently convert mixed expressions into a standard form for implementation with basic gates or programmable logic. The two most common canonical forms are sum-of-products (SOP) and product-of-sums (POS). This question asks which Boolean law lets us expand W(X + YZ) into SOP, where each term is a product (AND) of literals and the overall expression is a sum (OR) of those products.

Given Data / Assumptions:

• The expression is W(X + YZ).
• Variables W, X, Y, Z are Boolean (take values 0 or 1).
• Goal: express as SOP (sum of product terms).

Concept / Approach:

The key law is Boolean distribution, which lets a factor multiply (AND) into a sum (OR). The distributive law appears in two useful forms:

• A(B + C) = AB + AC
• A + BC = (A + B)(A + C) (the dual, for POS work)

Here, we need the first form to push W across the parentheses so that the result is a sum of product terms suitable for SOP implementation.

Step-by-Step Solution:

Verification / Alternative check:

You can construct a quick truth table for W, X, Y, Z and verify that F = 1 exactly when either WX = 1 or WYZ = 1. A Karnaugh map grouping would also show the same on-cells, confirming that distribution produced an equivalent SOP expression without changing functionality.

Why Other Options Are Wrong:

• Associative law changes grouping only, such as (A + B) + C = A + (B + C); it does not expand across a sum.
• Commutative law swaps order, such as AB = BA or A + B = B + A; it does not expand products over sums.
• Idempotent law (A + A = A, AA = A) simplifies duplicate literals, not distribute factors.
• “None of the above” is incorrect because distribution is exactly what is used.

Common Pitfalls:

• Stopping at WX + W(YZ) and forgetting that W(YZ) is already a valid product term WYZ; no further expansion is needed for SOP.
• Accidentally turning W + (YZ) into (W + Y)(W + Z), which is a POS transformation, not SOP.

Final Answer:

distributive law