# What is a hexadecimal decoder

## Hexadecimal code

**Origin / use:**The common number system that we use every day is the decimal system, based on 10, probably due to the fact that we have 10 fingers to count. For the numbers 0 to 9 we only need one digit, the 10 is then carried over and we need two digits, where the right digit (ones place) has the value 1 and the second right digit (tens place) has the value 10, etc. To get one So we take the 1st digit times 1, the 2nd times 10, the 3rd times 100, etc. from right to left and add the individual values.

Electronic circuits cannot actually count, and if so, then up to a maximum of 1, because they only know two states: on or off, symbolized in digits 0 or 1. The base is therefore two. Here, too, you can express any number by taking each digit from right to left times the value at the digit position to the base (1, 2, 4, 8, 16 etc.), but that results in long numbers very quickly, e.g. . B. 1111101000 (binary) for 1000 (decimal).

A compromise for "legibility" between human and computer is a number based on 16, with the values from right to left being 1, 16, 256, 4096, etc. The digits used are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, i.e. those that we already know from the decimal system plus AF for 10 (dec.) to 15 (dec.). If hex numbers have two digits, they are written with leading zeros, if they are single digits, so decimal '12' is hexadecimal '0C'.

Since the computer memory is divided into bytes (8 bits each), i.e. it holds values from 0 to 255 per byte, this division and groups of 2 hex digits each are used for these values. For certain registers or if you want to save larger numbers, there are also larger hex numbers with 4 hex digits (2 bytes = 1 word) for values from 0-65535 (16

^{4}) or 8 hex digits (4 bytes = double word) for values from 0-4,294,967,295 (16

^{8}) or -2.147.483.648 to +2147483647, if you also want to take negative numbers into account, then the first bit is used for the sign and 31 bits remain for the value itself.

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