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Binary-to-minterm conversion (variable order A, B, C, D): The 4-bit pattern 1010 corresponds to which product (minterm) term in SOP form?

Difficulty: Easy

A * B' * C * D'
A' * B * C' * D
A * B * C' * D
A' * B' * C * D'
A * B' * C' * D

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

Explanation:

Introduction / Context:
This item checks your ability to translate a binary assignment into a minterm (product) for a specified variable order. In standard SOP, each minterm includes all variables either complemented or uncomplemented to represent one unique row of the truth table.

Given Data / Assumptions:

Variable order is A, B, C, D (left to right).
Binary 1010 means A=1, B=0, C=1, D=0.
We want the corresponding product term.

Concept / Approach:
For a variable equal to 1, use the variable uncomplemented; for 0, use its complement. Combine all variables with * to form the minterm.

Step-by-Step Solution:

Step 1: Map bits: A=1 → A; B=0 → B'; C=1 → C; D=0 → D'.Step 2: Form the minterm: A * B' * C * D'.Step 3: Verify that the term uniquely identifies the 1010 row.

Verification / Alternative check:
This corresponds to minterm m10 (if A is the MSB). Expanding to decimal index confirms consistency with A B C D = 1 0 1 0.

Why Other Options Are Wrong:

A' * B * C' * D: Bit pattern 0 1 0 1, not 1 0 1 0.A * B * C' * D: Uses B=1 and D=1, contradicting 1010.A' * B' * C * D': Uses A=0, not 1.A * B' * C' * D: Uses C=0 and D=1, not 1 and 0.

Common Pitfalls:
Forgetting the stated variable order or flipping complement rules.

Binary-to-minterm conversion (variable order A, B, C, D): The 4-bit pattern 1010 corresponds to which product (minterm) term in SOP form?

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