Sum-of-products (SOP) implementation strategy: Which universal gate family most directly realizes SOP expressions with minimal complication, enabling two-level NAND–NAND realizations and easy inversion where needed?

Introduction / Context:The sum-of-products (SOP) form is one of the most common ways to describe Boolean functions for hardware realization. Engineers frequently translate an SOP expression into a two-level gate network. Choosing a universal gate family simplifies the build, reduces part types, and eases optimization.

Given Data / Assumptions:

• SOP means an OR (sum) of multiple AND (product) terms, possibly with complemented literals.
• We aim for a uniform implementation using a single gate type where possible.
• De Morgan’s laws permit inversion bubbles to be moved between levels to match available gates.

Concept / Approach:NAND gates are universal and particularly convenient for SOP. A product term can be created with a NAND followed by inversion; the final sum operation (OR) can be formed by a NAND whose inputs are the NANDed product terms with appropriate bubble placement. This yields a standard two-level NAND–NAND structure equivalent to AND–OR, but built entirely from NANDs.

Step-by-Step Solution:

Verification / Alternative check:Compare to a NOR–NOR approach. NOR is ideal for POS (product-of-sums) implementations. For SOP, NAND–NAND aligns naturally without extra inversion overhead.

Why Other Options Are Wrong:

Common Pitfalls:Mistaking NOR as equally suitable for SOP; forgetting bubble pushing when converting AND–OR to NAND–NAND; assuming inverters are always needed rather than using intrinsic NAND inversions.

Final Answer:NAND