Sum-of-Products (SOP) — Structural Advantage Which statement highlights a key practical advantage of expressing logic in sum-of-products (SOP) form for implementation with basic gates?
-
AAll logic circuits are reduced to nothing more than simple AND and OR operations.
-
BThe delay times are greatly reduced over other forms.
-
CNo signal must pass through more than two gates, not including inverters.
-
DThe maximum number of gates that any signal must pass through is reduced by a factor of two.
Answer
Correct Answer: No signal must pass through more than two gates, not including inverters.
Explanation
Introduction / Context:Sum-of-products (SOP) expresses a Boolean function as an OR of product terms. In a two-level realization, each product term is an AND of literals, and the final stage is a single OR combining those terms. This structure is widely used in PLDs and minimized gate designs.
Given Data / Assumptions:
- Two-level implementation: first level AND, second level OR.
- Inverters may be used to generate complemented literals but are not counted as logic levels in this comparison.
- Goal is to assess path depth from inputs to output.
Concept / Approach:In a canonical two-level SOP implementation, any input signal traverses at most an AND gate and then an OR gate to reach the output. This bounded depth is advantageous for timing predictability and is foundational in programmable logic device architectures.
Step-by-Step Solution:Express F as F = P1 + P2 + ... + Pk where each Pi is a product (AND) of literals.Route each input to the required AND gate(s) to form the product terms.Feed the outputs of all AND gates into a single OR gate.Hence, each signal path goes through at most two logic gates (AND then OR).
Verification / Alternative check:This property underlies classic two-level minimization methods (K-maps, Quine–McCluskey) and the structure of sum-of-products implementations in PLDs.
Why Other Options Are Wrong:
- All logic circuits are reduced to only AND/OR: Not universally true without potentially exploding the number of terms.
- Delay times greatly reduced: Not guaranteed; depends on fan-in and technology.
- Reduced by a factor of two: An arbitrary claim; the key is the fixed two-level structure.
Common Pitfalls:Counting inverters as logic levels, or assuming a specific delay advantage without considering gate fan-in and loading.
Final Answer:No signal must pass through more than two gates, not including inverters.