Perform arithmetic operations on binary numbers with step-by-step details
This binary calculator performs addition, subtraction, multiplication, and division on binary numbers (base 2). It validates that inputs contain only 0s and 1s, and presents results in binary, decimal, and hexadecimal formats with a clear step-by-step breakdown of the arithmetic.
Binary arithmetic follows the same principles as decimal arithmetic but uses only two digits (0 and 1). Addition uses carries, subtraction uses borrowing, multiplication is a series of shifts and adds, and division is repeated subtraction. Each operation is shown step by step.
Each binary digit represents a power of 2, starting from 2⁰ at the rightmost position. Multiply each digit by its corresponding power of 2 and sum the results. For example, 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11.
Binary is the fundamental number system used by computers. Every digital device processes data in binary form, where each 0 or 1 represents an electrical state (off/on). Understanding binary is essential for low-level programming and digital electronics.