Hexa Decimal

Base-16, using A-F for the digits 10-15. Natural for computer use, since 16 is a power of two and a 32-bit machine word is exactly described by eight hex digits.

The HistoryOfHex (slightly different, merge?):

tazzoz wrote:

> Can anyone please help me, i am really interested in learning about > the history of HEX and ASCII? Such as why they are used and how they > came about, etc?

Hex, short for "hexadecimal base counting", was invented in France in the year 770 AD. In that time Mervin, a famous wizard, became a counselor to King Charlemagne because he had 8 fingers on each hand.

Mervin could count faster than the other counselors and treasurers, because within a base he could go farther, using more symbols in less positions. When other mathematicians in the king's court had risen to 100, Mervin would only be at 0x64. This meant Mervin could express larger numbers in a smaller space.

But there was a more fundamental advantage. When King Charlemagne would divide his country into fiefdoms for taxation purposes, his treasurers would divide the country into 2 duchies, each of which were divided into 2 earldoms, each of which were divided into 2 counties, each of which divided into 2 lordships, each of which contained 2 vassalages.

This means the entire country consisted of 32 vassalages and 16 lordships. But, to Mervin, there were 0x20 vassalages, and 0x10 lordships. Put another way, because Mervin's total finger count was a power of a power of two, he could more easily divide and multiply. To divide by 16 he shifts right one base counting amount, and to divide by a power of two < than 16 he manipulates only one column without affecting the others.

Those with 10 fingers can multiply and divide by 10 easily, of course. But Mervin's technique maximizes the number of non-primes for whome multiplication and division resolve to only digit manipulations. We now refer to abstracts of this system as "binary".

Mervin takes his place with Charles Babbage and the Jaquard guy who invented the mechanically programmed loom as one of the founders of the theories that lead to modern programming

--PhlIp