For three variables A, B, C, write the canonical Sum-of-Minterms for Y = Σ m (1, 3, 5, 7). Which expression is correct?

Introduction / Context:
Canonical forms (Sum-of-Minterms and Product-of-Maxterms) are foundational in logic design, enabling systematic simplification and implementation using standard gates.

Given Data / Assumptions:

• Minterms: m(1, 3, 5, 7).
• Variables ordered as A (MSB), B, C (LSB).

Concept / Approach:

Each minterm index corresponds to the binary pattern of ABC. Index → bits: 1 → 001, 3 → 011, 5 → 101, 7 → 111. A 0 bit means complemented variable, a 1 bit means uncomplemented.

Step-by-Step Solution:

Verification / Alternative check:

Create a 3-variable truth table for indices 1,3,5,7 and confirm outputs are 1 only at those rows. K-map grouping also matches this canonical SOP.

Why Other Options Are Wrong:

• Options with any term having a wrong complemented/uncomplemented variable do not match the specified minterm index.
• Expressions including C' for indices whose LSB is 1 are invalid for this set.

Common Pitfalls:

Misordering variables (e.g., using C as MSB) and mixing up complements when translating index to literals.

Final Answer:

Y = A'B'C + A'BC + AB'C + ABC