Decimal to Binary Calculator
Enter a decimal integer to convert it to binary.
How to Convert Decimal to Binary
Method: repeated division by 2
- Divide the number by 2. Note the remainder (0 or 1).
- Repeat with the quotient until it reaches 0.
- Read remainders from bottom to top — that is the binary result.
Example: 42 → 21 R0 → 10 R1 → 5 R0 → 2 R1 → 1 R0 → 0 R1 → 101010
Quick reference
| Decimal | Binary | Hex |
|---|---|---|
| 1 | 1 | 1 |
| 8 | 1000 | 8 |
| 10 | 1010 | A |
| 16 | 10000 | 10 |
| 255 | 11111111 | FF |
Related Calculators
How to Convert Decimal to Binary
The standard method is repeated division by 2: divide the decimal number by 2, record the remainder (0 or 1), then divide the quotient by 2 again. Repeat until the quotient is 0. Read the remainders from bottom to top — that is your binary number. For example, converting 13: 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1 → read remainders bottom-up: 1101. Check: 1×8 + 1×4 + 0×2 + 1×1 = 13. ✓
Decimal to Binary Quick Reference
| Decimal | Binary | Decimal | Binary |
|---|---|---|---|
| 1 | 1 | 16 | 10000 |
| 5 | 101 | 32 | 100000 |
| 10 | 1010 | 64 | 1000000 |
| 15 | 1111 | 128 | 10000000 |
The Division-by-Two Method Explained
Converting a decimal integer to binary by repeated division is a systematic technique anyone can apply manually. Divide the decimal number by 2 and record the remainder, which will be either 0 or 1. Take the quotient and divide it by 2 again, recording the new remainder. Continue dividing until the quotient reaches 0. The binary equivalent is the sequence of remainders read from bottom to top (last remainder to first). For example, to convert 13 to binary: 13 divided by 2 gives quotient 6 remainder 1; 6 divided by 2 gives quotient 3 remainder 0; 3 divided by 2 gives quotient 1 remainder 1; 1 divided by 2 gives quotient 0 remainder 1. Reading remainders from bottom to top gives 1101, which is 13 in binary. Verify by expanding: 1 times 8 plus 1 times 4 plus 0 times 2 plus 1 times 1 equals 13. This method generalizes to any positive integer. For fractional parts, multiply by 2 repeatedly and record the integer part each time, reading from top to bottom for the binary fraction.
Decimal to Binary Conversion Reference Table
| Decimal | Binary | Check (sum of powers of 2) |
|---|---|---|
| 1 | 1 | 1 |
| 5 | 101 | 4 + 1 |
| 10 | 1010 | 8 + 2 |
| 16 | 10000 | 16 |
| 25 | 11001 | 16 + 8 + 1 |
| 64 | 1000000 | 64 |
| 100 | 1100100 | 64 + 32 + 4 |
| 255 | 11111111 | 128+64+32+16+8+4+2+1 |
Binary Representation in Computing
Computers store all data in binary form. A single binary digit is called a bit. Eight bits make one byte, which can represent 256 distinct values (0 through 255). Sixteen bits form a word capable of holding 65,536 values. Understanding how decimal numbers convert to binary is essential for working with low-level programming, network subnet masks, bitwise flags, and memory-mapped hardware registers. When you set file permissions on a Unix system with a command like chmod 755, each digit of 755 in octal corresponds to a three-bit binary group that defines read, write, and execute access. Recognizing this binary foundation clarifies many computing conventions that otherwise appear arbitrary.
