Tetradecimal

From Wikipedia, the free encyclopedia
Numeral systems by culture
Hindu–Arabic numerals
East Asian numerals
Alphabetic numerals
Other historical systems
Positional systems by base
Decimal (10)
Non-standard positional numeral systems
List of numeral systems

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.

Understanding the tetradecimal system can be difficult. Example: Starting with 100 (base 10), tetradecimal representations of decimal numbers are:

Base 10=Base 14

100 = 72

99 = 71

98 = 70

however

97 = 6D

this is the sixth cycle of the tetradecimal system, and it has come to the 'Dth' term.

so

6D = 6×14+D = 6×14+13 = 84+13 = 97

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

Base 14 is an analogue of 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
X 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

External links

This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.