Binary Calculator & Converter
Instantly convert and calculate binary, decimal, hexadecimal, and octal numbers. Free, accurate tool for developers, students, and computer science enthusiasts.
Calculate Your Binary Operations
Enter your values, select the number base, and choose an operation to get instant, precise conversions and calculations across all major numbering systems.
Calculation Details
Enter your numbers to see mathematical equivalents and results
Conversion Results
Calculated mathematical equivalents
Common Number Conversions
Standard equivalents for numbers 0 through 15 across binary, decimal, hexadecimal, and octal systems to help you quickly verify calculations.
| Decimal | Binary | Hexadecimal | Octal |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 8 | 10 |
| 9 | 1001 | 9 | 11 |
| 10 | 1010 | A | 12 |
| 11 | 1011 | B | 13 |
| 12 | 1100 | C | 14 |
| 13 | 1101 | D | 15 |
| 14 | 1110 | E | 16 |
| 15 | 1111 | F | 17 |
Binary Calculator FAQ
Everything you need to know about number systems, conversions, and bitwise operations.
A binary number is a number expressed in the base-2 numeral system, which uses only two symbols: 0 and 1. It is the fundamental language of computers and digital electronics, where each digit represents a power of 2.
To convert binary to decimal, multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right), and sum the results. For example, binary 101 is (1×2²) + (0×2¹) + (1×2⁰) = 4 + 0 + 1 = 5.
Bitwise operations (AND, OR, XOR, NOT) manipulate individual bits of binary numbers. They are heavily used in low-level programming, cryptography, network masking, and optimizing performance in software development.
Hexadecimal is a base-16 system using digits 0-9 and letters A-F, commonly used in programming for memory addresses and color codes. Octal is a base-8 system using digits 0-7, historically used in older computing systems and still seen in Unix file permissions.