Add, subtract, multiply, and divide binary numbers (Base 2), or convert freely between Binary and Decimal with step-by-step mathematical breakdowns and Two's Complement notation.
Perform base-2 arithmetic with automatic decimal, hex, and octal cross-conversions.
Convert base-2 binary strings to base-10 decimal numbers with positional power expansions.
Convert base-10 decimal numbers to base-2 binary strings with continuous division by 2.
The binary number system is a base-2 positional numeral system that uses only two symbols: 0 and 1 (binary digits or bits). Modern electronic computers use binary logic internally because electrical transistors can reliably represent two physical voltage states: ON (1) and OFF (0).
Two's complement is a mathematical technique used in computer architecture to represent signed negative integers. It allows computer hardware to perform addition and subtraction using the exact same arithmetic logic unit (ALU) circuitry without requiring separate subtraction hardware.
In binary fractions, bits to the right of the radix point represent negative powers of 2. For example, 0.1₂ = 2⁻¹ = 0.5, 0.01₂ = 2⁻² = 0.25, and 0.001₂ = 2⁻³ = 0.125. Therefore, 101.101₂ = 4 + 1 + 0.5 + 0.125 = 5.625.
Hexadecimal (Base 16) is a human-friendly compact representation of binary. Since 16 = 2⁴, exactly four binary bits (one nibble) map to a single hexadecimal digit (e.g., 1111₂ = 0xF).
Yes. The engine uses native JavaScript BigInt, enabling exact integer calculations for binary strings with hundreds of digits without overflow or truncation.