Binary Calculator
Perform binary arithmetic operations and convert between binary and decimal number systems.
Binary Arithmetic Operations
Perform addition, subtraction, multiplication, or division on two binary numbers.
Binary to Decimal Converter
Convert a binary number to decimal with a step-by-step breakdown.
Decimal to Binary Converter
Convert a decimal number to binary using the division method.
Quick Reference Table (0-20)
| Decimal | Binary | Decimal | Binary | Decimal | Binary |
|---|---|---|---|---|---|
| 0 | 0 | 7 | 111 | 14 | 1110 |
| 1 | 1 | 8 | 1000 | 15 | 1111 |
| 2 | 10 | 9 | 1001 | 16 | 10000 |
| 3 | 11 | 10 | 1010 | 17 | 10001 |
| 4 | 100 | 11 | 1011 | 18 | 10010 |
| 5 | 101 | 12 | 1100 | 19 | 10011 |
| 6 | 110 | 13 | 1101 | 20 | 10100 |
Understanding Binary Numbers
What is Binary?
Binary is a base-2 numeral system that uses only two digits: 0 and 1. Unlike the decimal system (base-10) that we use daily with digits 0-9, computers use binary because electronic circuits can easily represent two states: off (0) and on (1).
Each digit in a binary number is called a bit (binary digit). Eight bits form a byte, which can represent values from 0 to 255 (or 0000 0000 to 1111 1111 in binary).
Why Computers Use Binary
Computers use binary because it maps directly to electrical signals. A transistor can be either on (representing 1) or off (representing 0). This makes binary extremely reliable for data storage and processing.
All data in computers—text, images, videos, programs—is ultimately stored and processed as binary numbers.
Binary Arithmetic Rules
Addition
0 + 0 = 00 + 1 = 11 + 0 = 11 + 1 = 10 (carry 1)Subtraction
0 - 0 = 01 - 0 = 11 - 1 = 010 - 1 = 1 (borrow)Multiplication
0 × 0 = 00 × 1 = 01 × 0 = 01 × 1 = 1Division
0 ÷ 1 = 01 ÷ 1 = 1Works like decimaldivision by 2