Decimal to Binary Converter
Instantly convert any decimal (base 10) number to binary (base 2) with full step-by-step division breakdown and bit-length counter.
Quick Reference — Common Decimal to Binary Values
| Decimal | Binary | Decimal | Binary |
|---|---|---|---|
| 0 | 0 | 16 | 10000 |
| 1 | 1 | 32 | 100000 |
| 2 | 10 | 64 | 1000000 |
| 4 | 100 | 128 | 10000000 |
| 8 | 1000 | 255 | 11111111 |
| 10 | 1010 | 256 | 100000000 |
| 15 | 1111 | 1024 | 10000000000 |
What is a Decimal Number?
The decimal number system (base 10) is the standard counting system we use every day. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit position represents a power of 10. For example, the number 255 means (2 × 100) + (5 × 10) + (5 × 1).
What is Binary?
The binary number system (base 2) uses only two digits: 0 and 1. It is the native language of computers and digital electronics. Every calculation your computer performs is ultimately done in binary. Each binary digit is called a bit, and 8 bits form a byte.
How to Convert Decimal to Binary — Step by Step
The standard method is to divide by 2 repeatedly and read the remainders bottom-up:
- Divide the decimal number by 2
- Write down the remainder (0 or 1)
- Divide the quotient by 2 again
- Repeat until the quotient is 0
- Read the remainders from bottom to top — that is your binary number
Example: Convert 13 to binary:
13 ÷ 2 = 6 remainder 1 ← bit 0 (LSB) 6 ÷ 2 = 3 remainder 0 ← bit 1 3 ÷ 2 = 1 remainder 1 ← bit 2 1 ÷ 2 = 0 remainder 1 ← bit 3 (MSB) Result (read bottom-up): 1101â‚‚
Why Do Computers Use Binary?
Computers are built from billions of tiny switches called transistors. A transistor has only two states: on (1) or off (0). Binary perfectly maps to these two states, making it the most reliable and efficient system for digital electronics. All images, text, sound, and video you see on a computer is ultimately stored as a sequence of 0s and 1s.