Decimal To Binary
Use our free decimal to binary converter, binary to decimal calculator, Decimal number to binary. This Decimal to Binary Converter transforms base-10 numbers into binary (base-2) instantly. Enter any decimal integer, and the tool calculates its binary equivalent. Free, fast, and no installation required.
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How to convert decimal to binary: Manual Conversion Method
Divide the decimal number by 2
Record the quotient and remainder (0 or 1).
Repeat with the new quotient until it becomes 0.
Read the remainders backward (bottom to top) for the binary result.
Example: Convert 13 to Binary
| Step | Division | Quotient | Remainder |
|---|---|---|---|
| 1 | 13 ÷ 2 | 6 | 1 (LSB) |
| 2 | 6 ÷ 2 | 3 | 0 |
| 3 | 3 ÷ 2 | 1 | 1 |
| 4 | 1 ÷ 2 | 0 | 1 (MSB) |
Result: Read remainders ↑ to ↓ → 1101 ✅
Shortcut: Powers of 2 Subtraction
List powers of 2 (from highest ≤ your number):
- 128,64,32,16,8,4,2,1128,64,32,16,8,4,2,1
Subtract largest power possible; mark 1 if used, 0 if skipped.
Example: Convert 25 to Binary
Powers: 16 (≤25), 8 (≤9), 4 (≤1→skip), 2 (≤1→skip), 1 (≤1):
text
16 → 25-16=9 → **1** 8 → 9-8=1 → **1** 4 → skipped → **0** 2 → skipped → **0** 1 → 1-1=0 → **1**
Result: 11001 ✅
Decimal to Binary Table
| Decimal | Binary |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 8 | 1000 |