Convert to binary: 23

Your answer must start with a 1 (no leading zeros).

Question

Convert to binary: 23

Your answer must start with a 1 (no leading zeros).

BlackTom AI · Accepted Answer

23 = 16 + 4 + 2 + 1, and these are powers of two (2^4, 2^2, 2^1, 2^0), so the binary digits for 2^4..2^0 are 1 0 1 1 1, giving 10111.

Relevant concepts:
- Binary representation expresses a number as a sum of powers of two, each power corresponding to a bit (0 or 1).
- Alternatively, repeated division by 2 produces remainder bits; reading remainders from last to first gives the binary digits.

Step-by-step reasoning (division-by-2 method, showing intermediate steps):
1) 23 ÷ 2 = 11 remainder 1
2) 11 ÷ 2 = 5 remainder 1
3) 5 ÷ 2 = 2 remainder 1
4) 2 ÷ 2 = 1 remainder 0
5) 1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top: 1 0 1 1 1 → 10111.

Verification by powers of two (showing all intermediate sums):
Bits (from left to right) correspond to 2^4, 2^3, 2^2, 2^1, 2^0:
1·2^4 + 0·2^3 + 1·2^2 + 1·2^1 + 1·2^0
= 1·16 + 0·8 + 1·4 + 1·2 + 1·1
= 16 + 0 + 4 + 2 + 1
= 23

Why this is correct:
- The binary string 10111 uniquely sums to 23 as shown, and it starts with 1 (no leading zeros), satisfying the requirement.

Why other possible strings are incorrect:
- Any shorter string like 1011 (11) or 10110 (22) does not sum to 23.
- Adding leading zeros (e.g., 0010111) represents the same value but violates the “start with a 1 (no leading zeros)” requirement.
- Any different bit pattern producing a different sum (e.g., 11111 = 31) is wrong.

Conclusion: The correct binary representation of 23 is 10111, which matches the provided answer.

Convert to binary: 23 Your answer must start with a 1 (no leading zeros).Short answer

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