# The Echoes of the Mind (48-2) Bases

Bases

4 times 5 is 12, and 4 times 6 is 13, and 4 times 7 is – oh dear! I shall never get to 20 at that rate. ~ Alice in Alice’s Adventures in Wonderland (1865) by English novelist Lewis Carroll

Our hands have 10 fingers, and so a base-10 number system seems natural for tallying, which is where arithmetic got its start. The ancient Chinese and Egyptians used base-10.

Some early societies employed other bases. The ancient Sumerians and Babylonians had sexagesimal (base-60) systems, which simplified handling fractions in calculations.

The Mayans (1500 BCE~1700) had a vigesimal (base-20) system. Mayan priests used a mixed numeral system of base-20 and base-360. The Mayan calendar had 360 days in a year.

The modern decimal (base-10) system eventuated in Europe by the 15th century with the incorporation of zero into the Hindu-Arabic number system.

Owing to memory storage being of bits either on or off, electronic computers are built upon a binary (base-2) system. To achieve decimal handling capability, bits are concatenated into a hexadecimal (base-16) system.