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).简答题

类似问题

Convert decimal 54807 to binary

What is 89 in regular binary? (canvas may autofill commas, but don't worry, just ignore them)

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

What bit pattern is represented by the following hexadecimal pattern: 6A3 Answer must contain 4 bits per symbol.

Use hexadecimal notation to represent the following bit pattern: 1101110000111111 Letters in your answer should be capitalized.

Perform the following addition in binary notation: 1011.01 + 1.101

valid = 7 * 2 – 5 / 3;

num = 17 / 2.0 + 4;

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单