Sum-of-products (SOP) form in digital logic Which statement highlights a key practical advantage of writing a Boolean function in SOP form?

Introduction / Context:
Simplifying Boolean expressions into sum-of-products (SOP) form is a cornerstone of digital circuit design. The SOP format maps directly to a two-level implementation using AND gates feeding a single OR gate (with optional input inverters), which is attractive for predictable timing and straightforward hardware realization.

Given Data / Assumptions:

• SOP means a logical sum (OR) of product terms (ANDs of literals).
• Implementation considered is the classical two-level AND–OR structure with optional input inversion.
• Gate delays are counted as the number of logic levels a signal traverses, excluding any input inverter.

Concept / Approach:
Any Boolean function expressed in SOP can be realized by first generating each product term using AND gates (level 1), then combining these terms with a single OR gate (level 2). Because input inversion can be done prior to level 1, each signal passes through at most two logic levels (AND then OR) to reach the output.

Step-by-Step Solution:
Recognize SOP structure: F = P1 + P2 + ... + Pn where each Pi is a product of literals.Hardware mapping: literals → (optional NOT); products → AND stage; sum → OR stage.Level counting: a given input feeds at most one AND and then the final OR, totaling two logic levels (excluding the initial inverter).Therefore, the salient advantage is the two-level path for any input signal.

Verification / Alternative check:
Karnaugh map (K-map) minimization often yields simplified SOP. The minimized SOP still maps to two levels, confirming the property regardless of expression size.

Why Other Options Are Wrong:
“All circuits reduced to simple AND/OR only”: while SOP maps to AND–OR, other optimizations or technologies (e.g., NAND/NOR-only) may be preferred; the unique timing benefit is the two-level depth.“Delay times greatly reduced over other forms”: not universally guaranteed compared with, for example, optimized multi-level logic.“Reduced by a factor of two”: not a general rule; the important guarantee is two logical levels, not a numeric factor against any arbitrary baseline.

Common Pitfalls:
Confusing SOP with POS (product-of-sums) or neglecting that input inversions are not counted as gate levels in many conventions.

Final Answer:
No signal must pass through more than two gates, not including inverters.