What is 21 in binary?
21₁₀ converted to binary is 10101₂. The complete working for this exact number is below — or type a different number into the decimal to binary converter and watch it happen live.
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How to convert 21 to binary, step by step
Keep dividing 21 by 2 and writing down each remainder. The remainders, read in reverse, are the answer.
| Number | ÷ 2 | Quotient | Remainder |
|---|---|---|---|
| 21 | 2 | 10 | 1 |
| 10 | 2 | 5 | 0 |
| 5 | 2 | 2 | 1 |
| 2 | 2 | 1 | 0 |
| 1 | 2 | 0 | 1 |
Reading the remainder column from the bottom up gives 10101, so 21₁₀ = 10101₂. Check it back: 16 + 4 + 1 = 21 — the 1 bits add up to 21.
In short: 21 ÷ 2 = 10 r 1 → 10 ÷ 2 = 5 r 0 → 5 ÷ 2 = 2 r 1 → 2 ÷ 2 = 1 r 0 → 1 ÷ 2 = 0 r 1 → read bottom-up: 10101₂
Frequently asked questions
How do you write 21 in binary?
Divide 21 by 2 over and over, noting each remainder: 21 ÷ 2 = 10 r1, 10 ÷ 2 = 5 r0, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1. Reading the remainders from last to first gives 10101, so 21₁₀ = 10101₂.
How long is 21 in binary?
21 in binary is 10101, which is 5 bits long. It ends in 1 because 21 is odd — the last bit of any binary number tells you odd (1) or even (0).
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