Difficulty: Easy
Correct Answer: 154
Explanation:
Introduction / Context:
Binary-to-decimal conversion is a fundamental skill in digital electronics and computer science. Each binary digit (bit) represents a power of 2, and the decimal value is the sum of those powers where bits are 1.
Given Data / Assumptions:
Concept / Approach:
For a binary string b7 b6 b5 b4 b3 b2 b1 b0, the decimal value is sum(bi * 2^i) for i from 0 to 7. Only positions with bi = 1 contribute to the sum.
Step-by-Step Solution:
Verification / Alternative check:
Group into nibbles: 1001 1010 → 0x9A in hex. Hex 0x9A = 9*16 + 10 = 144 + 10 = 154, confirming the result.
Why Other Options Are Wrong:
Common Pitfalls:
Forgetting that the leftmost bit is the highest power of 2, or mixing up 2^3=8 and 2^4=16.
Final Answer:
154
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