Binary Calculator
Convert between binary, decimal, octal, and hexadecimal. Perform binary arithmetic with step-by-step working.
About Binary Calculator
Binary is the base-2 number system, using only digits 0 and 1. Every digit (bit) represents a power of 2: the rightmost bit is 2⁰ (1), the next is 2¹ (2), then 2² (4), and so on. For example, 1101 in binary equals 1×8 + 1×4 + 0×2 + 1×1 = 13 in decimal. Binary is the native language of digital computers because transistors have two states: off (0) and on (1).
Hexadecimal (base 16) is a convenient shorthand for binary: each hex digit maps to exactly four binary bits, making it easy to read large binary values. Octal (base 8) uses three bits per digit. Programmers regularly switch between these bases when working with memory addresses, color codes, and file permissions.
Binary arithmetic follows the same rules as decimal arithmetic, with carries happening when a column's sum reaches 2 instead of 10. For subtraction, borrows work similarly. Our Hex Calculator covers hexadecimal-specific operations. Use the Big Number Calculator for very large integer arithmetic.
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For a related calculation, use Hex Calculator to convert between hexadecimal, decimal, binary, and octal. Perform arithmetic on hex numbers. Alternatively, use Number Sequence Calculator to calculate the nth term, sum, and list of terms for arithmetic and geometric sequences.
For the underlying method, read Binary and Hexadecimal Explained: A Beginner's Guide.