Free Binary Calculator Online
Convert between binary, decimal, octal, and hexadecimal — or perform binary arithmetic and bitwise operations. This free binary calculator shows results in all four number bases simultaneously.
Enter a number in any base and see its representation in binary, decimal, octal, and hexadecimal.
Binary
Number Base Conversion
How the Binary Calculator Works
The binary calculator operates in two modes. In Convert mode, you enter a number in any base (binary, decimal, octal, or hex), and it parses the input using that base's radix. It then displays the equivalent value in all four number systems using JavaScript's built-in parseInt and toString functions.
In Arithmetic mode, you provide two binary numbers and choose an operation. The binary calculator converts both to decimal internally, performs the math, and then converts the result back to all four bases. Bitwise operations (AND, OR, XOR) work at the bit level — comparing each pair of corresponding bits.
Number Base Reference
Binary Arithmetic Explained
Related Math Tools
Why Use This Free Binary Calculator?
- Convert + Arithmetic modes
- All four bases at once
- Bitwise AND, OR, XOR
- Input validation
- Always free, no sign-up
What People Use a Binary Calculator For
Programming
Developers work with binary and hex regularly — debugging memory addresses, reading file headers, parsing network packets, and setting bitflags. The binary calculator lets you verify conversions quickly instead of doing mental math.
Networking
IP addresses and subnet masks are binary at their core. Understanding that 255.255.255.0 is 11111111.11111111.11111111.00000000 makes subnetting intuitive. Use the binary calculator to verify mask calculations and bitwise AND operations.
Computer Science Studies
Binary arithmetic is foundational in CS courses. From understanding how CPUs add numbers to learning two's complement and floating point representation, this binary calculator helps you check your homework and build intuition.
Binary Number System Essentials
Understanding binary is key to understanding how computers think.
Everything Is Bits
Every piece of data on your computer — text, images, video, code — is ultimately a sequence of 0s and 1s. A single binary digit (bit) is the smallest unit of data. Eight bits make a byte, which can represent 256 different values (0-255).
Powers of Two
Each position in a binary number represents a power of 2, right to left: 1, 2, 4, 8, 16, 32, 64, 128... This is why computer memory comes in powers of 2 (256 MB, 512 MB, 1 GB, etc.) and why the binary calculator is built around these fundamentals.
Hex = Compact Binary
Hexadecimal exists because it is a shorthand for binary. Four bits map to one hex digit: 0000=0, 1111=F. This makes hex 4× more compact than binary while preserving a direct bit-level correspondence.
Frequently Asked Questions
This free binary calculator is provided for informational and educational purposes. Results use JavaScript's standard number precision (53-bit integers). For extremely large numbers, consider a specialized big-integer tool.
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