The History of Number Bases
Why Base 10?
Humans have 10 fingers, so counting in base 10 (decimal) emerged independently across many cultures. The decimal system we use today was developed by Indian mathematicians around the 6th century CE and transmitted to the Western world by Arab scholars — which is why our digits are called 'Arabic numerals'.
Base 60: The Babylonian Legacy
The ancient Babylonians used base 60 (sexagesimal). Why 60? Because it's divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 — making fractions much cleaner. We still live with this system: 60 seconds in a minute, 60 minutes in an hour, 360 degrees in a circle. Base 60 has survived 4,000 years.
Binary: The Language of Computers
Binary (base 2) was described mathematically by Gottfried Wilhelm Leibniz in 1703, but it didn't become practically important until electronic computers emerged in the 1940s. Electrical circuits naturally have two states — on or off, 1 or 0 — making binary the perfect language for digital machines. All modern computing is built on binary at the hardware level.
Octal and Hexadecimal
Octal (base 8) was used in early computing because early computers grouped bits in triplets. Hexadecimal (base 16, using digits 0–9 and letters A–F) became standard because it groups bits in sets of 4, making binary easier to read — one hex digit represents exactly four binary digits. Web colors (#FF5733), memory addresses, and color codes are all written in hex.
The Mayan Base 20
The Mayan civilization used a base-20 (vigesimal) number system — likely because they counted fingers and toes. Remarkably, the Maya independently invented the concept of zero, around 350 CE, one of the great intellectual achievements in mathematical history. Zero allowed positional number systems to work cleanly — without it, modern arithmetic is impossible.