Base 11

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The undecimal (base-11) positional notation system is based on the number eleven, rather than ten as in decimal or eight in octal and so on. It is not a commonly used system. Undecimal requires eleven symbols representing the decimal numbers 0 through 10. For example, if the symbol for 10 were 'A', the decimal numbers 0 to 24 in undecimal would be: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 20, 21, 22. The undecimal number 1A3 would be 234 in decimal.

Base 11 addition table[edit]

+ 1 2 3 4 5 6 7 8 9 A 10 11 12
1 2 3 4 5 6 7 8 9 A 10 11 12 13
2 3 4 5 6 7 8 9 A 10 11 12 13 14
3 4 5 6 7 8 9 A 10 11 12 13 14 15
4 5 6 7 8 9 A 10 11 12 13 14 15 16
5 6 7 8 9 A 10 11 12 13 14 15 16 17
6 7 8 9 A 10 11 12 13 14 15 16 17 18
7 8 9 A 10 11 12 13 14 15 16 17 18 19
8 9 A 10 11 12 13 14 15 16 17 18 19 1A
9 A 10 11 12 13 14 15 16 17 18 19 1A 20
A 10 11 12 13 14 15 16 17 18 19 1A 20 21
10 11 12 13 14 15 16 17 18 19 1A 20 21 22
11 12 13 14 15 16 17 18 19 1A 20 21 22 23
12 13 14 15 16 17 18 19 1A 20 21 22 23 24

Base 11 multiplication table[edit]

X 1 2 3 4 5 6 7 8 9 A 10 11 12
1 1 2 3 4 5 6 7 8 9 A 10 11 12
2 2 4 6 8 A 11 13 15 17 19 20 22 24
3 3 6 9 11 14 17 1A 22 25 28 30 33 36
4 4 8 11 15 19 22 26 2A 33 37 40 44 48
5 5 A 14 19 23 28 32 37 41 46 50 55 5A
6 6 11 17 22 28 33 39 44 4A 55 60 66 71
7 7 13 1A 26 32 39 45 51 58 64 70 77 83
8 8 15 22 2A 37 44 51 59 66 73 80 88 95
9 9 17 25 33 41 4A 58 66 74 82 90 99 A7
A A 19 28 37 46 55 64 73 82 91 A0 AA 109
10 10 20 30 40 50 60 70 80 90 A0 100 110 120
11 11 22 33 44 55 66 77 88 99 AA 110 121 132
12 12 24 36 48 5A 71 83 95 A7 109 120 132 144

Base 11 in fiction[edit]

Base 11 systems appear in several science fiction stories: Carl Sagan's novel Contact references a message "hidden" inside pi that is most striking in base 11, as that permits it to be displayed in binary code. Also the fictional Psychlos (in L. Ron Hubbard's book Battlefield Earth) have a base-11 counting system.

In the television series Babylon 5, the Minbari use base-11 mathematics, according to the show's creator.

ISBN check digit[edit]

The check digit for ISBN-10 is found as the result of taking modulo 11. Since this could give 11 possible results, the digit "X" is used in place of "10". (The newer ISBN-13 standard uses modulo 10, so no extra digits are required.)

See also[edit]

External links[edit]