Add, subtract, multiply and divide binary numbers — with step-by-step workings and automatic conversion to decimal, hexadecimal and octal.
Enter your figures and click Calculate to see your results.
Enter two binary numbers (only digits 0 and 1) and select the operation — results appear in binary, decimal, hex and octal.
Press the Calculate button. All results appear instantly — no page reload, no waiting.
Results appear in the panel on the right with all key values clearly labelled. Use Copy to grab the result or Download to save a text file.
Binary addition uses only 0 and 1. Rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1). Work column by column from right to left, exactly like decimal addition but carrying when the sum reaches 2 instead of 10.
Multiply each binary digit by 2 raised to the power of its position (0 on the right). For binary 1011: (1×8)+(0×4)+(1×2)+(1×1) = 11 in decimal. This calculator performs the conversion automatically for all four bases.
Binary maps directly to two electronic states: on (1) and off (0). Every piece of data — text, images, programs, video — is stored as sequences of binary digits (bits). Groups of 8 bits form a byte, capable of representing 256 values. Binary arithmetic is simple to implement in physical hardware.
Hexadecimal (base-16) uses digits 0–9 and letters A–F. Each hex digit represents exactly 4 binary bits, making hex a compact human-readable way to represent binary. One byte = two hex digits. Hex is used everywhere in programming: memory addresses, colour codes, machine code and cryptographic hashes.
The calculator uses JavaScript's built-in integer arithmetic, which supports exact integers up to 2⁵³ − 1 (about 9 quadrillion) for basic operations. For larger values, the Big Number Calculator on this page uses BigInt for arbitrary precision arithmetic.
