What is 103 in unsigned binary? (canvas may autofill commas, just ignore them)

Question

BlackTom AI · Accepted Answer

Unsigned binary uses powers of two for each bit position (2^0, 2^1, 2^2, ...). Converting 103 to binary is done by successive division by 2 and recording remainders; the binary digits are those remainders read from last (most significant) to first (least significant).

1) Relevant knowledge points and concepts
- Each binary digit (bit) represents a power of two.
- For unsigned integers, the value = sum(bit_i * 2^i).
- Division-by-2 method: divide the decimal number by 2 repeatedly; remainders (0 or 1) are the binary digits from least significant to most significant.

2) Complete reasoning process step by step
Perform repeated division of 103 by 2 and record remainders:
- 103 ÷ 2 = 51 remainder 1
- 51 ÷ 2 = 25 remainder 1
- 25 ÷ 2 = 12 remainder 1
- 12 ÷ 2 = 6 remainder 0
- 6 ÷ 2 = 3 remainder 0
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1

3) Intermediate steps shown
Remainders from first to last: 1, 1, 1, 0, 0, 1, 1
Read bottom-up (most significant to least): 1100111

4) Why the correct answer is correct
Convert 1100111 back to decimal to verify:
- Positions (from right): 2^0..2^6
- Value = 1·2^6 + 1·2^5 + 0·2^4 + 0·2^3 + 1·2^2 + 1·2^1 + 1·2^0
- = 64 + 32 + 0 + 0 + 4 + 2 + 1 = 103
Therefore 1100111 correctly represents 103 in unsigned binary.

5) Why other common alternatives are incorrect
- 1000111 would equal 71 (64 + 0 + 0 + 0 + 4 + 2 + 1), not 103.
- 1101001 equals 105, not 103.
- 01100111 is an 8-bit form with a leading zero; it represents the same numeric value but is not the exact 7-bit string given as the expected answer. Leading zeros are allowed but the canonical minimal form is 1100111.

6) Conclusion
The unsigned binary representation of 103 is 1100111, which matches the provided answer.

What is 103 in unsigned binary? (canvas may autofill commas, just ignore them)简答题

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