Hexadecimal
Proposed (not decided): when written alongside dozenal, hexadecimal (base 16, used in computing) keeps X and E for ten and eleven, and the four digits after them take the next letters, A B C D. This dozenal hex counts 0-9 X E A B C D.
Why: X and E then mean the same thing in both bases, so nobody has to remember that hex E is fourteen while dozenal E is eleven. A B C D are free, because dozenal uses no other letters.
Advantage: one set of digits covers both bases: dozenal is 0-E, and hex is the same digits plus four.
| Binary | Standard hex | Dozenal hex | Dozenal | Decimal |
|---|---|---|---|---|
| 0000 | 0 | 0 | 0 | 0 |
| 0001 | 1 | 1 | 1 | 1 |
| 0010 | 2 | 2 | 2 | 2 |
| 0011 | 3 | 3 | 3 | 3 |
| 0100 | 4 | 4 | 4 | 4 |
| 0101 | 5 | 5 | 5 | 5 |
| 0110 | 6 | 6 | 6 | 6 |
| 0111 | 7 | 7 | 7 | 7 |
| 1000 | 8 | 8 | 8 | 8 |
| 1001 | 9 | 9 | 9 | 9 |
| 1010 | A | X | X | 10 |
| 1011 | B | E | E | 11 |
| 1100 | C | A | 10 | 12 |
| 1101 | D | B | 11 | 13 |
| 1110 | E | C | 12 | 14 |
| 1111 | F | D | 13 | 15 |
- Watch: in standard hex A-D mean ten to thirteen, but here they mean twelve to fifteen. Mark which is meant (standard hex keeps its 0x prefix) wherever both could appear
- Every hex (and binary) fraction ends in dozenal: 100 (144 dec) is 0x90, a multiple of 0x10 (16 dec), so each hex place needs at most two dozenal places (0x0.1 = 0;09)
- Not the other way: thirds repeat in hex, as they do in binary and decimal. Quarters are the common ground: 0x0.4 = 0;3 = 0.25 (dec)