To convert a decimal number to binary, divide it by 2 repeatedly and collect the remainders. Read those remainders from the last division to the first — that sequence is the binary number. Decimal 25 converts to 11001 in four division steps.
The Division Method
Here is the full conversion for 25:
| Step | Dividend | ÷ 2 | Quotient | Remainder |
|---|---|---|---|---|
| 1 | 25 | ÷ 2 | 12 | 1 |
| 2 | 12 | ÷ 2 | 6 | 0 |
| 3 | 6 | ÷ 2 | 3 | 0 |
| 4 | 3 | ÷ 2 | 1 | 1 |
| 5 | 1 | ÷ 2 | 0 | 1 |
Read the remainders from bottom to top: 1, 1, 0, 0, 1 → 11001.
Check: 16 + 8 + 0 + 0 + 1 = 25. ✓
Second Example: Converting 100
| Step | Dividend | Quotient | Remainder |
|---|---|---|---|
| 1 | 100 | 50 | 0 |
| 2 | 50 | 25 | 0 |
| 3 | 25 | 12 | 1 |
| 4 | 12 | 6 | 0 |
| 5 | 6 | 3 | 0 |
| 6 | 3 | 1 | 1 |
| 7 | 1 | 0 | 1 |
Bottom to top: 1, 1, 0, 0, 1, 0, 0 → 1100100.
Check: 64 + 32 + 0 + 0 + 4 + 0 + 0 = 100. ✓
As a padded 8-bit byte: 01100100.
The Subtraction Method (Alternative)
Start from the largest power of 2 that fits into your number. Write a 1, subtract, then repeat for the remainder. Fill every skipped power of 2 with a 0.
Converting 156:
| Power of 2 | Value | Fits? | Bit | Running total |
|---|---|---|---|---|
| 2⁷ | 128 | Yes | 1 | 156 − 128 = 28 |
| 2⁶ | 64 | No | 0 | 28 |
| 2⁵ | 32 | No | 0 | 28 |
| 2⁴ | 16 | Yes | 1 | 28 − 16 = 12 |
| 2³ | 8 | Yes | 1 | 12 − 8 = 4 |
| 2² | 4 | Yes | 1 | 4 − 4 = 0 |
| 2¹ | 2 | No | 0 | 0 |
| 2⁰ | 1 | No | 0 | 0 |
Reading top to bottom: 10011100. Check: 128 + 16 + 8 + 4 = 156. ✓
Quick Reference: Common Decimal-to-Binary Conversions
| Decimal | Binary | Notes |
|---|---|---|
| 0 | 00000000 | All zeros |
| 1 | 00000001 | Lowest non-zero byte |
| 10 | 00001010 | Decimal ten |
| 16 | 00010000 | First power of 2 above 15 |
| 32 | 00100000 | Space character in ASCII |
| 65 | 01000001 | Letter A in ASCII |
| 128 | 10000000 | Half of 255 |
| 255 | 11111111 | Max single-byte value |
Converting Text to Binary
To convert a word to binary, convert each character’s ASCII decimal code to binary. For “Hi”:
- H = 72 =
01001000 - i = 105 =
01101001
Full binary string: 01001000 01101001
Use the binary translator to convert any text or number instantly. For the reverse — reading a binary number back to decimal — see How to Read Binary.
When to Pad to 8 Bits
In data transmission and storage, individual bytes are always 8 bits wide. If your conversion produces fewer than 8 digits (as with 25 = 11001), pad with leading zeros to get 00011001. This ensures every character occupies exactly one byte in memory, avoiding misalignment errors when computers read a file.