Hex characters 0-F don't visually provide any information about the underlying binary. I can't tell from reading 0-F representations of hex if a specific bit is set or not. It's necessary to convert to binary to notice things like parity set to odd/even/none. But raw binary isn't compact enough to easily look at.
Kaktovik Hex is a compact binary and hex representation based on some of the ideas behind Kaktovik Inupiaq. It supports the same visual arithmetic as Inupiaq, but also supports things like visual XOR. The bits of each nibble are represented as either | (for ones), V (for 2), or empty (for 0). The lower two bits are on the bottom, the upper two are rotated on the top. Every symbol can be written without lifting a pen.
It's just the first draft. I have a bunch of notes and I started a font file that repalces 0-9 A-F with these characters, but my font creation skills are somewhat lacking. I may upload that later just for completeness.
Edit: I have used it a bit for dates to see how it feels, and I've done some math with it. The deviation in the 9 character, and addition of a dot, comes from experimenting and finding that it looks a little to close to 13. I've switched the direction of the different sections a few times to make it easy to write.
It took a few iterations to get here, so this is maybe 1.5st draft. I'll try to add some follow up when I get a chance.