I was never happy with any of the ways of writing hexadecimal digits, so I developed my own for fun.

Numerals 1 - 15, the "+" symbol represents 0.

Obviously each of the features represent a bit of a 4-bit word.

The area of the "hole" inside the feature roughly corresponds to the value of that bit... 1, 2, 4, and 8.

Each bit feature is rather distinctive, so it's easy to come across a bunch of numbers written on a napkin and figure out which way is "up" (unlike some other hexadecimal numeral systems I've seen on the net).

Sorry that the "0" came out looking exactly like a "+" symbol... All of the digits basically have the "+" in them, so it made sense to use the empty frame without any bit features as 0. As a bonus, when you write a big number like 65536 (which would look like "1++++") you'd just write a long dash and go back and cross it with as many 0 digits as you needed.

Haven't come up with a clever unconventional way of writing out these digits, other than the same way we use arabic numerals now... read from left to right starting with the most significant digit. I'd like to come up with some wacky recursive way of arranging numerals radially, but I'd expect that'd make it tough to print and serialize.

There are a few neat visual symmetries with the way the 4-bit features are arranged radially in increasing significance. It corresponds to a typical radial coordinate system, where the feature in Quadrant I represents 1, Quadrant II represents 2, Quadrant III represents 4, and Quadrant IV represents 8.

These symmetries kind of make it easier to learn and remember the digits and make them unique with respect to each other. This should help people learn, characterize, and process these symbols somewhat faster, than, say, a simpler set of binary 1's and 0's that would be more natural for a computer to process, while still retaining most of the neat math tricks/simplifications that you can take advantage of when using binary math.

Of course, it's trivial to see whether a number is even or odd simply by looking for the 1 bit in Quadrant 1.

It's also fairly easy to inspect whether a number is divisible by 4 and 8 simply by making sure that quadrants II and III in the 1's place are all also blank, respectively.

Digits divisible by 3 make triangles (OK, you have to squint your eyes a bit) where the base is formed by bit feature in two adjacent quadrants. The "3" triangle points down, the "6" triangle points right, the "9" triangle points up. "15" is special, of course :P

Digits "5" and "10" have features on opposite quadrants, so they both look like figure-eights.

Of the digits made of features in three quadrants, most of them are prime ("7", "11", and "13"). This leaves "14" as the only digit among the first 16 digits that isn't somehow special. Which kinda makes it special :>

Anyway, I'm starting to stretch. Plenty of other people have expounded on some of the advantages of learning to count and do math in hexadecimal instead of decimal, the least of which includes being able to poke at the internals of a computer without translation layers.