Base Converter

A number base (or radix) defines how many unique digits are used to represent numbers. Decimal (base 10) uses digits 0-9, binary (base 2) uses 0 and 1, octal (base 8) uses 0-7, and hexadecimal (base 16) uses 0-9 plus A-F. Each base is a different way to express the same numeric value.

Computers use binary because their hardware is built on transistors that have two states: on (1) and off (0). All data in a computer — text, images, programs — is ultimately stored and processed as sequences of binary digits (bits). Understanding binary helps developers work with low-level operations, bitwise logic, and memory management.

Web colors use hexadecimal notation to represent RGB values. A hex color like #FF5733 breaks down to FF (255 red), 57 (87 green), and 33 (51 blue). Each pair of hex digits represents a color channel value from 0 to 255. Hexadecimal is used because it compactly represents byte values (0-255) in just two characters.

Octal (base 8) is primarily used in Unix/Linux file permissions. The permission value 755 means the owner has read, write, and execute (7 = 111 in binary), while the group and others have read and execute (5 = 101 in binary). Octal provides a compact way to represent three-bit groups.

Two's complement is the standard method for representing signed (positive and negative) integers in binary. The most significant bit indicates the sign (0 for positive, 1 for negative). To negate a number, you invert all bits and add 1. For example, in 8-bit two's complement, -1 is represented as 11111111 (255 in unsigned). This tool converts unsigned positive integers only.