Decimal to 8-bit binary — encode the value with leading zeros if needed. Task: Convert 187₁₀ to an 8-bit binary representation.
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
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A10111011
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B11011101
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C10111101
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D10111100
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E10111010
Answer
Correct Answer: 10111011
Explanation
Introduction / Context:Encoding a decimal integer as an 8-bit binary pattern is common when writing to registers, configuring peripherals, or defining bit masks. The 8-bit form explicitly shows each bit from 2^7 to 2^0.
Given Data / Assumptions:
- Decimal value: 187
- Target width: 8 bits (MSB first)
Concept / Approach:Decompose 187 into powers of two ≤ 128. Mark a 1 for each included power and 0 otherwise to build the 8-bit string. Alternatively, perform repeated division by 2 and pad to 8 bits.
Step-by-Step Solution:
Largest power ≤ 187 is 128 (2^7): remainder 59Next 64 (2^6): not used (0); remainder stays 59Use 32 (2^5): remainder 27Use 16 (2^4): remainder 11Use 8 (2^3): remainder 3Use 4 (2^2): not used (0); remainder 3Use 2 (2^1): remainder 1Use 1 (2^0): remainder 0Bits: 1 0 1 1 1 0 1 1 ⇒ 10111011Verification / Alternative check:Sum the active weights: 128 + 32 + 16 + 8 + 2 + 1 = 187. Also, a calculator check in binary mode will show 187 → 10111011₂.
Why Other Options Are Wrong:
- 11011101, 10111101, 10111100, 10111010: each flips or misses one or more required bit positions.
Common Pitfalls:
- Forgetting the 64’s place is 0 here, or misplacing the 4’s place (which is 0).
Final Answer:10111011