2-bit vector operation (recovered intent = addition): Given 2-bit unsigned vectors [A] = 10 and [B] = 01 (A is MSB), compute [A] + [B].
Digital Electronics
Digital Arithmetic Operations and Circuits
Difficulty: Easy
Choose an option
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A[00]
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B00
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C11
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D[11]
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E[10] with carry
Answer
Correct Answer: [11]
Explanation
Introduction / Context:The original stem omitted the operator; by Recovery-First we adopt the standard teaching example aligned with nearby items: 2-bit vector addition. Treat [A]=10 (binary 2) and [B]=01 (binary 1) as unsigned and add them.
Given Data / Assumptions:
- Vectors are 2 bits wide, A is MSB.
- Unsigned addition; no saturation.
- Result reported as a 2-bit vector (no overflow here).
Concept / Approach:2 + 1 = 3. In binary, 3 is 11, which fits in 2 bits; no extra carry beyond the 2-bit width is generated.
Step-by-Step Solution:
LSB: 0 + 1 = 1, carry 0.MSB: 1 + 0 + carry 0 = 1.Concatenate → [11].Verification / Alternative check:Decimal check: 2 + 1 = 3 → binary 11.
Why Other Options Are Wrong:
[00]/00: Sum is not zero.11 (without brackets) lacks the vector format; still the same value but formatting inconsistent.[10] with carry: Incorrect; no carry occurs.Common Pitfalls:Misreading the MSB/LSB order.
Final Answer:[11]