What is 1000 in binary?
1000₁₀ converted to binary is 1111101000₂. 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.
Try it yourself — instant converter
See the steps for your number
How to convert 1000 to binary, step by step
Keep dividing 1000 by 2 and writing down each remainder. The remainders, read in reverse, are the answer.
| Number | ÷ 2 | Quotient | Remainder |
|---|---|---|---|
| 1000 | 2 | 500 | 0 |
| 500 | 2 | 250 | 0 |
| 250 | 2 | 125 | 0 |
| 125 | 2 | 62 | 1 |
| 62 | 2 | 31 | 0 |
| 31 | 2 | 15 | 1 |
| 15 | 2 | 7 | 1 |
| 7 | 2 | 3 | 1 |
| 3 | 2 | 1 | 1 |
| 1 | 2 | 0 | 1 |
Reading the remainder column from the bottom up gives 1111101000, so 1000₁₀ = 1111101000₂. Check it back: 512 + 256 + 128 + 64 + 32 + 8 = 1000 — the 1 bits add up to 1000.
In short: 1000 ÷ 2 = 500 r 0 → 500 ÷ 2 = 250 r 0 → 250 ÷ 2 = 125 r 0 → 125 ÷ 2 = 62 r 1 → 62 ÷ 2 = 31 r 0 → 31 ÷ 2 = 15 r 1 → 15 ÷ 2 = 7 r 1 → 7 ÷ 2 = 3 r 1 → 3 ÷ 2 = 1 r 1 → 1 ÷ 2 = 0 r 1 → read bottom-up: 1111101000₂
Frequently asked questions
How do you write 1000 in binary?
Divide 1000 by 2 over and over, noting each remainder: 1000 ÷ 2 = 500 r0, 500 ÷ 2 = 250 r0, 250 ÷ 2 = 125 r0, 125 ÷ 2 = 62 r1, 62 ÷ 2 = 31 r0, 31 ÷ 2 = 15 r1, 15 ÷ 2 = 7 r1, 7 ÷ 2 = 3 r1, 3 ÷ 2 = 1 r1, 1 ÷ 2 = 0 r1. Reading the remainders from last to first gives 1111101000, so 1000₁₀ = 1111101000₂.
How long is 1000 in binary?
1000 in binary is 1111101000, which is 10 bits long. It ends in 0 because 1000 is even — the last bit of any binary number tells you odd (1) or even (0).
Keep converting
Popular values
10 in binary · 25 in binary · 42 in binary · 50 in binary · 100 in binary · 255 in binary