# hexadecimal system (HEX)

The hexadecimal system (HEX) should actually be called the sedecimal system, since it is derived from the Latin sedecem, which stands for sixteen. The name hexadecimal system has been taken over from the American.

The hexadecimal system is a number system with base 16. The numbers of the decimal system are used as number symbols, i.e. the digits 0 to 9, supplemented by the first six letters of the alphabet, A to F. This notation has the advantage that it is unique and consists of only one character. In addition, all sixteen numbers can be represented in the binary system with four bits. The digit valence is given with 0 to 9, for two-digit numbers the letters A to F are used. A corresponds to the number 10, B corresponds to 1+1 C to 12, D to 13, E to 14 and F to 15.

Hexadecimal numbers are written in the same way as the decimal system, so that the lowest digit means `16^0`, the digit to the left `16^1` = 16, the next one `16^2` = 256, then `16^3` = 4096 and so on. If you convert a hexadecimal number into a decimal number, you have to add the exponent to each digit and add the resulting digits. Example: the hexadecimal number 2A9 consists of the sum of the digits '2*16^2 + A*16^1 + 9*16^0'. This is equal to the sum of 512 + 160 + 9 and is 681. Important: No computer works in the hexadecimal system. It is only a notation to better remember long binary strings, i.e. ones and zeros, and to reduce the probability of error.

Two-digit hexadecimal numbers are most commonly found because they represent the eight bits of a byte. For example, the binary number 0011 1101 would be written in hexadecimal 3D = `3 * 16^1+13 * 16^0 = 48 + 13 = 61`. The two halves of the byte are called half byte or nibble.