Binary Calculator 🔢
Perform arithmetic operations on binary numbers
Binary Calculator – Guide & Info
What is Binary?
Binary is a number system with base 2, using only 0 and 1. Computers use binary to store and process data.
Addition & Subtraction
Binary addition and subtraction follow rules similar to decimal arithmetic but carry/borrow only when exceeding 1. Example: 101 + 11 = 1000
Multiplication & Division
Binary multiplication works like repeated addition. Division works like repeated subtraction. Example: 110 × 10 = 1100
Negative Binary
Negative numbers are usually represented with two's complement in computing. Here we show results with a '-' sign for simplicity.
Decimal Conversion
Binary numbers can be converted to decimal for calculation, then converted back to binary for the result. Example: 1010 (binary) = 10 (decimal).
Real-World Use
Binary arithmetic is foundational in computer science, digital electronics, programming, and logic circuits.
Example Calculations
Example 1: Addition
- Binary 1 = 1010
- Binary 2 = 1101
- 1010 + 1101 = 10111 (binary) = 23 (decimal)
Example 2: Subtraction
- Binary 1 = 1100
- Binary 2 = 101
- 1100 − 101 = 111 (binary) = 7 (decimal)
Example 3: Multiplication
- Binary 1 = 101
- Binary 2 = 11
- 101 × 11 = 1111 (binary) = 15 (decimal)
Example 4: Division
- Binary 1 = 1101
- Binary 2 = 10
- 1101 ÷ 10 = 110 (binary) remainder 1 = 6 remainder 1 (decimal)
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