Questions About Memorizing Binary Numbers

I’m interested in finding out if there are any systems that utilizes the natural hexadecimal breakdown of binary sequences?
Any help would be greatly appreciated.

Are you looking for something like this hexadecimal system?

Kind of like that. It’s a start, but doesn’t take advantage of the hex lettering,

Binary…decimal…Hex…Peg
0000…0…0…s/z

0001…1…1…t/d

0010…2…2…n

0011…3…3…m

0100…4…4…r

0101…5…5…l

0110…6…6…j(soft)/sh/yadda

0111…7…7…K (hard C and G)

1000…8…8…f/v

1001…9…9…p/b

1010…10…A…??

1011…11…B…??

1100…12…C…??

1101…13…D…??

1110…14…E…??

1111…15…F…??

Whatever system works it should utilitze the hex letters, I could be wrong, but my understanding is that the contests use 20 binary digits per row. That should break down to 5 pegs (and therefore require fewer links to retain).