(Redirected from Base 14)

The tetradecimal (base-14) positional notation system is based on the number fourteen. Comparatively, the decimal system is based on the number ten, the hexadecimal system is based on the number sixteen, and so on. Other names used for the base-14 system include quadrodecimal and quattuordecimal.

Tetradecimal requires fourteen symbols. Since there are only ten common decimal digits, the notation can be extended by using letters A, B, C and D to represent values 10, 11, 12 and 13, respectively. For example, decimal values 0 to 20 in tetradecimal would be: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, 10, 11, 12, 13, 14, 15, 16. The tetradecimal number 373 would be 689 in decimal, as 3(142) + 7(14) + 3 = 588 + 98 + 3 = 689.

This numeric base is seldom used. It finds applications in fields such as programming for the HP 9100A/B calculator,[1] image processing applications.[2]

Base 14 is related to bases 4, 6, 9, 10 (decimal), 15, 21, and 25 as all are small semiprimes.

## Base 14 multiplication table

 (decimal) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 × 1 2 3 4 5 6 7 8 9 A B C D 10 1 1 2 3 4 5 6 7 8 9 A B C D 10 2 2 4 6 8 A C 10 12 14 16 18 1A 1C 20 3 3 6 9 C 11 14 17 1A 1D 22 25 28 2B 30 4 4 8 C 12 16 1A 20 24 28 2C 32 36 3A 40 5 5 A 11 16 1B 22 27 2C 33 38 3D 44 49 50 6 6 C 14 1A 22 28 30 36 3C 44 4A 52 58 60 7 7 10 17 20 27 30 37 40 47 50 57 60 67 70 8 8 12 1A 24 2C 36 40 48 52 5A 64 6C 76 80 9 9 14 1D 28 33 3C 47 52 5B 66 71 7A 85 90 A A 16 22 2C 38 44 50 5A 66 72 7C 88 94 A0 B B 18 25 32 3D 4A 57 64 71 7C 89 96 A3 B0 C C 1A 28 36 44 52 60 6C 7A 88 96 A4 B2 C0 D D 1C 2B 3A 49 58 67 76 85 94 A3 B2 C1 D0 10 10 20 30 40 50 60 70 80 90 A0 B0 C0 D0 100

## Notes

1. ^ See the HP Museum website
2. ^ See one patent at Free Patents Online