Decimal to Binary Conversion
This converter helps you convert decimal numbers (base-10) into binary (base-2), and vice versa.
How to Use This Converter
- Enter a decimal number like
42to get the binary result - Or enter binary (e.g.,
101010) to convert it to decimal
You can switch between decimal and binary easily using this tool.
Understanding the Conversion
Decimal is the standard base-10 number system using digits 0-9. Binary is base-2 and only uses 0 and 1.
Each digit in binary represents a power of 2, starting from the right. Here's how the conversion works:
- 42 in decimal → 101010 in binary
- Explanation: 42 = 32 + 8 + 2 = 2⁵ + 2³ + 2¹
Example
Convert decimal 19 to binary:
- Find the largest power of 2 less than or equal to 19 → 16 (2⁴)
- Subtract 16: 19 - 16 = 3
- Next power of 2: 2 (2¹), remaining: 1
- Next: 1 (2⁰), remaining: 0
- Binary: 10011
Result: 1910 = 100112
Binary Table (0-15)
| Decimal | Binary |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
Where Binary Is Used
Binary is the fundamental language of computers and digital electronics. Everything from numbers, characters, images, and sounds are represented as sequences of 0s and 1s in binary.
Use this tool to understand and convert numbers into binary for:
- Programming and software development
- Computer architecture and low-level debugging
- Electronics and logic gate design
- Learning how computers actually work