Binary Calculator
Perform arithmetic operations with binary numbers and convert between binary and decimal. Perfect for computer science, programming, and digital electronics.
Binary Calculator & Converter
Binary Examples
Click on these links to see instant calculations with common binary operations:
Binary Number System
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, where each digit represents a power of 2.
Binary Arithmetic Rules
| Operation | Rules | Examples |
|---|---|---|
| Addition | 0+0=0, 0+1=1, 1+0=1, 1+1=10 | 1010 + 1100 = 10110 |
| Subtraction | 0-0=0, 1-0=1, 1-1=0, 0-1=1 (borrow) | 1100 - 1010 = 0010 |
| Multiplication | 0×0=0, 0×1=0, 1×0=0, 1×1=1 | 101 × 11 = 1111 |
| Division | Similar to decimal long division | 1100 ÷ 11 = 100 |
Binary to Decimal Conversion
To convert binary to decimal, multiply each digit by 2 raised to its position power (starting from 0 on the right) and sum the results.
Example: 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13₁₀
Decimal to Binary Conversion
To convert decimal to binary, repeatedly divide by 2 and collect the remainders in reverse order.
Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 → 1101₂
- Computer Science: Understanding binary operations and computer arithmetic
- Programming: Bitwise operations, data structures, and algorithm optimization
- Digital Electronics: Logic gates, circuit design, and digital signal processing
- Networking: IP addresses, subnet masks, and network calculations
- Cryptography: Binary operations in encryption and security algorithms
Frequently Asked Questions
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.
How do you add binary numbers?
Binary addition follows simple rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1). Add from right to left, carrying over when needed.
How do you convert binary to decimal?
To convert binary to decimal, multiply each digit by 2 raised to its position power (starting from 0 on the right) and sum the results.