Binary Calculator
Convert numbers between binary, decimal, hex and octal. Perform arithmetic and bitwise operations on binary numbers.
Free Binary Calculator — Add, Subtract, Multiply & Convert Number Bases
Binary arithmetic is fundamental to computer science, digital electronics, and low-level programming. Whether you are a student learning number systems, a developer working with bitwise operations, or an engineer debugging binary data, this free Binary Calculator performs arithmetic in binary and converts between binary, decimal, hexadecimal, and octal instantly.
Enter binary numbers to add, subtract, multiply, or divide. The calculator shows results in binary and automatically converts to decimal, hex, and octal simultaneously — saving time switching between tools.
Understanding binary, hexadecimal, and their relationships is essential for programming in C/C++, embedded systems development, network engineering (subnet masks), color manipulation (hex color codes), and cryptography.
Number Base Systems
Binary (Base 2). Uses only 0 and 1. Direct representation of digital logic states. Used internally by all computers and microprocessors.
Decimal (Base 10). The everyday number system using digits 0–9. What humans naturally use for counting.
Hexadecimal (Base 16). Uses 0–9 and A–F. Each hex digit = 4 binary digits. Used for memory addresses, color codes (CSS hex colors), bytecode, and programming.
Octal (Base 8). Uses digits 0–7. Each octal digit = 3 binary digits. Used in Unix/Linux file permissions (chmod 755) and some legacy systems.
Related Tools
- Hex Calculator – Convert and calculate in hexadecimal.
- Decimal to ASCII – Convert decimal numbers to ASCII characters.
- Binary to Text – Convert binary code to readable text.
Frequently Asked Questions
What is binary arithmetic?
Math using only 0 and 1. The foundation of all digital computing.
How to convert binary to decimal?
Multiply each bit by 2^position and sum. e.g., 1011 = 8+0+2+1 = 11.
Why use hexadecimal?
Each hex digit represents 4 binary digits — compact shorthand for binary data. Used in color codes, memory addresses, bytecode.
Is this free?
Yes. Completely free, no account needed.