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 based decimal 3 2 1 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 97 98 99 1 1 1 1 2 999 1 Elementary arithmetic 30 80 210 0 0 20 ignored the carry based result is 110 20 31 51 0 1 21 ignored the carry based result is 41 27 34 51 7 4 21 ignored the carry based result is 41 26 34 40 6 4 0 borrowed 1 due to no carry based result is 40 31 21 42 1 1 2 borrowed 1 due to no carry based result is 32 1 5 1 5 1 5 5 0 borrowed 1 due to no carry based result is 1 0 0 4 20 4 0 4 24 ignored the carry 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 based result is 1944 HTH Thanks iiy