Classify the Boolean form of the expression AB + CD in terms of canonical implementation styles used in programmable logic.

Difficulty: Easy

Correct Answer: SOP

Explanation:


Introduction / Context:
Two common canonical Boolean forms are sum-of-products (SOP) and product-of-sums (POS). Recognizing which form a given expression belongs to helps you map it to specific hardware resources in PLDs and CPLDs.


Given Data / Assumptions:

  • Expression: AB + CD.
  • We need to categorize it by canonical form, not by device type.


Concept / Approach:
In SOP, multiple product terms (ANDs of literals) are ORed together. In POS, multiple sum terms (ORs of literals) are ANDed together. AB and CD are products (ANDs). Joining them with + indicates a sum (OR) of those products. Therefore, AB + CD is SOP.


Step-by-Step Solution:
Identify each term: AB (A*B) is a product; CD (C*D) is a product.Combine via + → OR of product terms.Conclude: AB + CD is a sum-of-products (SOP).


Verification / Alternative check:
Truth-table or Karnaugh-map implementations naturally produce SOP minimizations where each implicant corresponds to a product term ORed together.


Why Other Options Are Wrong:
PAL and GAL are device types, not Boolean forms. POS would look like (A + B)(C + D), not AB + CD.


Common Pitfalls:
Confusing hardware acronyms with algebraic forms; forgetting that the + symbol represents OR while adjacency represents AND.


Final Answer:
SOP

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion