Hexadecimal to Decimal Converter

Hexadecimal (hex) is a base-16 number system that uses 16 symbols: the digits 0-9 and the letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15). Hex is widely used in computing because one hex digit represents exactly four binary digits (bits), making it a compact way to express binary values. Hex values are often prefixed with '0x' (in C/JavaScript) or '#' (in CSS colors).

Multiply each hex digit by 16 raised to the power of its position (from right, starting at 0). Sum all the results. For example, 1A3 in hex: 3 x 16^0 = 3, A (10) x 16^1 = 160, 1 x 16^2 = 256. Total = 256 + 160 + 3 = 419 in decimal.

Divide the decimal number by 16 repeatedly, noting the remainder at each step. The remainders (read in reverse order) form the hex number. Remainders of 10-15 are written as A-F. For example, 419 / 16 = 26 remainder 3, 26 / 16 = 1 remainder 10 (A), 1 / 16 = 0 remainder 1. Reading remainders in reverse: 1, A, 3 = 1A3 in hex.

Hex is used extensively in computing for: memory addresses (e.g., 0x7FFF0000), color codes in HTML/CSS (e.g., #FF5733), machine code and assembly language, error codes and debugging, representing Unicode code points (e.g., U+1F600), and network addresses (e.g., MAC addresses like 00:1A:2B:3C:4D:5E). Its compact representation of binary data makes it ideal for low-level programming.

The largest single hex digit is F, which equals 15 in decimal (1111 in binary). Two hex digits can represent values from 00 (0) to FF (255), which is why bytes (8 bits, values 0-255) are commonly written as two hex digits. For example, 0xFF = 255, the maximum value of an unsigned 8-bit integer.