VetoVeto

Hexadecimal system

The hexadecimal system is a numeral system with base sixteen. It is the official numeral system of VetoVeto. Hexadecimal can be shortened to hex.

Representation

The hexadecimal system uses sixteen distinct symbols to represent the numerals. Nowadays, it is common practice to use 0 to 9 and A to F to count to fifteen in hexadecimal. Decimal numerals are denoted with a subscript 10, whereas hexadecimal numerals are denoted with a subscript 16. For instance, 1010 corresponds to A16. See the table for more examples.

Decimal Hexadecimal
110 116
210 216
210 216
310 316
410 416
510 516
610 616
710 716
810 816
910 916
1010 A16
1110 B16
1210 C16
1310 D16
1410 E16
1510 F16
1610 1016
3210 2016

Negative hexadecimal numbers work similar to negative decimal numbers. For instance, -1010 corresponds to -A16. Rules regarding multiplication of negative numbers are not different either, e.g. -510 × 210 = -1010 = -A16.

Hexadecimal fractions

As the hexadecimal numeral system uses base sixteen that does not easily translate to base 10, several decimal fractions do not have a simple hexadecimal representation and vice versa. In base ten we can easily divide each number in tenths: 0.110, 0.210 and so on. Conversely, we divide each number in sixteenths in hexadecimal: 0.116 = 1/1610 = 0.062516. A half is five tenths in decimal, thus 5/1010 = 0.510. A half is 8 sixteenths in hexadecimal, thus 8/1016 = 0.816. Nine tenths is 9/1010 = 0.910, but this 0.E66...16 in hexadecimal, where 6 is a repeating numeral.

In fact, most decimal fractions have a corresponding hexadecimal fraction with a repeating numeral. For instance, 0.110 corresponds to 0.199...16 where 9 is a repeating numeral.

Use in languages

The hexadecimal system is used in computing as there is a one-to-one correspondence between one hexadecimal digit and four binary digits. Besides applications in computing, the hexadecimal system does not see much use in everyday spoken and written languages of Earth, however.

Hexadecimal is the official counting system in the vast majority of languages of VetoVeto, such as Qromean and Sygvaraæn.