Difficulty: Easy
Correct Answer: 18₁₀
Explanation:
Introduction / Context:
Converting between binary and decimal is a foundational skill for interpreting addresses, register contents, and configuration fields in digital systems. Short binary words can be converted mentally by weighting each bit position by powers of two.
Given Data / Assumptions:
Concept / Approach:
Each binary 1 contributes its positional weight; zeros contribute nothing. Sum all active weights to obtain the decimal value.
Step-by-Step Solution:
Write weights: from right to left: 2^0=1, 2^1=2, 2^2=4, 2^3=8, 2^4=16.Map bits: 1 0 0 1 0 corresponds to 2^4 + 2^1 = 16 + 2.Add contributions: 16 + 2 = 18.Therefore, 10010(2) = 18(10).
Verification / Alternative check:
Convert back: 18 / 2 gives remainders 0,1,0,0,1 (in reverse), yielding 10010(2), confirming the result.
Why Other Options Are Wrong:
Common Pitfalls:
Final Answer:
18₁₀
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