Number Base Converter

A number base (radix) is the number of digits in the numeral system. Base 10 (decimal) uses digits 0-9. Base 2 (binary) uses 0,1. Base 16 (hexadecimal) uses 0-9 and A-F. Base n uses n digits from 0 to n-1, with letters extending beyond 9.

Base 36 uses all 36 alphanumeric characters: 0-9 and A-Z. It is the most compact way to represent numbers using standard keyboard characters. Example: 1000 in decimal = RS in base 36. URL shorteners and ID systems often use base 36 or base 62 for compact, URL-safe IDs.

Two-step method: (1) convert the source number to decimal, (2) convert from decimal to the target base. To decimal: multiply each digit by base^position and sum. From decimal: repeatedly divide by target base, collect remainders bottom-up. This calculator does both steps.

Base 60 was used by ancient Babylonians and is still used for time (60 seconds/minute, 60 minutes/hour) and angles (60 arcminutes/degree). 60 has many divisors (1,2,3,4,5,6,10,12,15,20,30,60), making it convenient for division.

Computers use binary because electronic circuits have two states: on/off (1/0). Binary is perfect for digital logic. Hexadecimal is used as a compact representation: each hex digit = exactly 4 binary bits, making conversion trivial. One byte (8 bits) = two hex digits. Octal was also used historically (each octal digit = 3 bits).