Binary Calculator
Perform binary arithmetic and convert between binary, decimal, octal, and hexadecimal number systems.
Binary Operations
Calculation Results
0
base 2
0
base 10
0
base 8
0
base 16
💡 Binary System: Binary uses only two digits: 0 and 1. It's the foundation of all computer systems and digital electronics.
What is Binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. It's the fundamental language of computers and digital systems. Every piece of data in a computer is ultimately represented in binary form.
Binary Arithmetic Operations
Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (0 carry 1)
Example: 1010 + 1100 = 10110
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (0 carry 1)
Example: 1010 + 1100 = 10110
Binary Subtraction
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 (borrow 1)
Example: 1100 - 1010 = 0010
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 (borrow 1)
Example: 1100 - 1010 = 0010
Binary Multiplication
0 × 0 = 0
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1
Example: 1010 × 1100 = 1111000
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1
Example: 1010 × 1100 = 1111000
Binary Division
Binary division follows the same long division process as decimal, but simpler since you only deal with 0 and 1.
Number System Conversions
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
Why Binary Matters
- Computer Science: All data in computers is stored and processed in binary.
- Digital Electronics: Circuits use binary states (on/off, high/low voltage).
- Networking: IP addresses and subnet masks use binary.
- Cryptography: Encryption algorithms operate on binary data.
References
- Khan Academy. "Binary Numbers." 2026.
- GeeksforGeeks. "Binary Arithmetic." 2026.