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 One-based numeration 
There's an interesting numeration called One-based numeration, which could be any numeral system that is counted from one, and it's usually compared to the widely used Zero-based numeration. This numeration defines the number ten as single digit, which is written as 0. But I don't think it's very efficient for arithmetic, what do you think about the numeration?
1-based binary:     -01 -0 -1 X 1 0 01 00 011 010 001 000 0111 0110 0101 0100 0011 0010 0001 ...
1-based hexadecimal: -3 -2 -1 X 1 2  3  4  5   6   7   8    9    A    B    C    D    E    F  0 21 22 23 24 .. 71 72 73  74  75  76 .. 4F7  4F8
1-based decimal:     -3 -2 -1 X 1 2  3  4  5   6   7   8    9    0   21   22   23   24   25 26 27 28 29 20 .. 07 08 09  00 211 212 .. 009  000
Ø-based decimal:     -3 -2 -1 Ø 1 2  3  4  5   6   7   8    9   1Ø   11   12   13   14   15 16 17 18 19 2Ø .. 97 98 99 1ØØ 1Ø1 1Ø2 .. 999 1ØØØ
Elementary arithmetic:
30 + 80 = 210 (0+0=20, ignored the carry) // Ø-based result is 110
20 + 31 = 51 (0+1=21, ignored the carry) // Ø-based result is 41
27 + 34 = 51 (7+4=21, ignored the carry) // Ø-based result is 41
26 + 34 = 40 (6+4=0, borrowed 1 due to no carry) // Ø-based result is 40
31 + 21 = 42 (1+1=2, borrowed 1 due to no carry) // Ø-based result is 32
1.5 + 1.5 = 1 (5+5=0, borrowed 1 due to no carry) // Ø-based result is 1
0 + 0.4 = 20.4 (0+4=24, ignored the carry) // Ø-based result is 19.4
Multiplication table:
+ 1-based decimal multiplication table x  1  2  3  4  5  6  7  8  9  0 1  1  2  3  4  5  6  7  8  9  0 2  2  4  6  8  0  22  24  26  28  20 3  3  6  9  22  25  28  31  34  37  30 4  4  8  22  26  20  34  38  42  46  40 5  5  0  25  20  35  30  45  40  55  50 6  6  22  28  34  30  46  52  58  64  60 7  7  24  31  38  45  52  59  66  73  70 8  8  26  34  42  40  58  66  74  82  80 9  9  28  37  46  55  64  73  82  91  90 0  0  20  30  40  50  60  70  80  90  00

For example, 353 x 8 = (3-1)00 x 8 + (5-1)0 x 8 + 3 x 8 = 2600 + 420 + 34 = 2020 + 34 = 2054 (Ø-based result is 1944)

HTH & Thanks, iiy "