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Standard SOP expansion (variables A, B, C): Convert F = A + B'*C into standard SOP form where each product term contains all variables.

Difficulty: Medium

A'*B'*C + A*B'*C' + A*B'*C + A*B*C' + A*B*C
A'*B*C' + A*B*C
A + B'*C
A' + B + C'
A*B + B'*C

Correct Answer: A'*B'*C + A*B'*C' + A*B'*C + A*B*C' + A*B*C

Explanation:

Introduction / Context:
Standard SOP requires every product term to include all variables. For three variables A, B, C, the function F = A + B'*C must be expanded so that each term has A, B, and C explicitly either complemented or not.

Given Data / Assumptions:

F = A + B'*C.
Variables: A, B, C.

Concept / Approach:
A alone covers all cases where A=1 (regardless of B and C), which corresponds to minterms m4, m5, m6, m7 (for ordering A as MSB). The term B'*C with A=0 adds minterm m1 (A=0, B=0, C=1). Combining yields a sum of specific minterms, each written as a full three-literal product.

Step-by-Step Solution:

Step 1: List minterms for A=1: m4 (100), m5 (101), m6 (110), m7 (111).Step 2: List minterm for A=0, B=0, C=1: m1 (001) from B'*C with A=0.Step 3: Write standard SOP: A'*B'*C (m1) + A*B'*C' (m4) + A*B'*C (m5) + A*B*C' (m6) + A*B*C (m7).

Verification / Alternative check:
Plotting on a 3-variable K-map shows four cells for A=1 and one cell for A=0,B=0,C=1, matching the expanded expression.

Why Other Options Are Wrong:

A'*B*C' + A*B*C: Incomplete coverage; misses many minterms with A=1.A + B'*C: This is the original non-standard expression.A' + B + C': Not SOP and not equivalent.A*B + B'*C: Not standard SOP, and not equivalent.

Common Pitfalls:
Forgetting that a standard term must include all variables; also double-counting minterms already covered by A.

Standard SOP expansion (variables A, B, C): Convert F = A + B'*C into standard SOP form where each product term contains all variables.

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