Who invented hexagonal numerical system?

Answer 1

I know of no such system; however, there is the hexadecimal number system which uses base 16 as opposed to base 10 - ie every digit can contain one of the sixteen decimal numbers 0-15 (with 10-15 usually represented as the first 6 letters in either upper case as A-F or lower case as a-f).

It is difficult to say if anyone invented it as such as using different bases have been around for a long-long time. I guess that we use a decimal (base 10 system) as we have 10 "fingers" (2 are thumbs) across our two hands. Other historic peoples used different based systems: The Mayans used base 20 (vigesimal) and the Babylonians used base 60 (sexagesimal) which we still use today (with relation to time (using the colon as a place value separator between the decimal numbers 0-59 of each sexagesimal digit, a time (using the 24 hour clock) of the form hh:mm:ss is the number of seconds since midnight in base 60) and measuring angles in degrees). The French also have some historic use of the vigesimal system as can be seen from the French for 80: "quatre-vingts" which is literally "four twenties".

When digital computers came along each memory location has two states: on/off or charge/nocharge or high/low which can be represented using two base 2 (binary) digits 1 and 0. However, to make it more useful these binary digits (or bits) are clumped together into sets of 8 (known as bytes). Bytes can be clumped together to make "words" which can be 2 bytes (16 bits), 4 bytes (32 bits), 8 bytes (64 bits), etc long.

When writing out the contents of memory locations, using binary can be very tedious (and not obvious to us as we're used to decimals) so a byte of memory can be written using a decimal number (0-255). Similarly 2 bytes of memory can be written out using decimal (0-65535).

But knowing the bit pattern (binary number) for memory is often useful but from decimal this requires quite a bit of calculation. Thus other bases which are a power of 2 are used; specifically base 8 (octal) and base 16 (hexadecimal). Octal is a natural choice for some circumstances, for example for *nix (Unix, Linux, etc) when dealing with file permissions are they are stored in sets of 3 bits; Similarly the old DEC-10 used a 36-bit word which is exactly 12 octal digits long (every word is 0-0777777777777), but also 9 hexadecimal digits (every word is 0-0xFFFFFFFFF).

However, with a byte, there are 8 bits so it is not quite 3 octal digits long - a byte has the octal values 0-0377. But hexadecimal is extremely useful as each digit is exactly 4 bits long. Thus a byte can be split into two hexadecimal digits (0-0xFF); half a byte is known as a nybble - each nybble is a hexadecimal digit. Similarly, most computers these days use a multiple of bytes as a word length; as each byte is exactly 2 hexadecimal digits, the word of the computer uses an exact number of hexadecimal digits.

Answer 2

Nobody did because there is no such system.