# How are hex codes calculated

## Hexadecimal number system (hex code)

Large binary numbers have the disadvantage that they are very confusing.
To remedy this, the hexadecimal system was introduced.
4 bits of a binary number are replaced by a hexadecimal character.
Since a 4-bit binary number can have 16 states, but we only know 10 decimal numbers, 6 letters have been added to the hexadecimal number system.

Nominal values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Base: 16
Largest face value: F.
Significance: 160 = 1, 161 = 16, 162 = 256, etc.

This table is used for a better understanding of the counting method in the hexadecimal number system. Each 4 binary digits form a hexadecimal digit.

000000
100011
200102
300113
401004
501015
601106
701117
810008
910019
101010A.
111011B.
121100C.
131101D.
141110E.
151111F.

### Hexadecimal numbers in computer engineering

In computer technology, the dual number system is decisive. Sometimes the hexadecimal system is also used. Usually for a clearer representation of large dual numbers. Long bit sequences of 4 bits each are grouped and converted into a hexadecimal number. In this way, a long sequence of 1 and 0 results in a shorter hexadecimal number. For easier readability, hexadecimal numbers are then grouped again in groups of 2 or 4.
Hexadecimal numbers or the hexadecimal representation is another form of representation of bit sequences.

010100001010110000111111 Bit sequence grouped bit sequence Conversion to hex numbers grouped hex numbers

The hexadecimal system or the sixteen system is used for a clearer and more compact representation of long bit sequences. It is also used in assembler programming for addressing I / O and memory modules.

### Spelling of the hexadecimal numbers

Hexadecimal numbers are marked with a "16" as an index or a preceding dollar sign (\$). Other spellings with "h" or "H" are inconsistent and therefore not correct and are only acceptable in exceptional cases.

• 10016 (correct spelling)
• \$ 100 (correct spelling)
• 0x100 (correct spelling)
• 100h (wrong spelling)
• 100H (incorrect spelling)

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