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number system

All number systems are defined by the numerical value of the character set and the place value. The place value of a single digit depends on its own value and on the position in the number. Each digit of a number has a basic value by which the digit is multiplied.

The character set of a number system depends on the base number. In the case of the decimal system with base 10, it consists of ten digits. The octal system has a base of 8 and consists of eight digits and the dual system consists of two digits.

Binary system

Binary system

Number systems that can be applied in computers and data networks should consist of only two states for digital processing, like the binary system: either an electrical voltage is present or not, "1" or "0". That is why any kind of digitallogical data processing is based on the binary system.

Analogous to the decimal system, the bit with the lowest significance, the least significant bit (LSB), is located on the far right of the binary system and has the value 2exp0 = 1. The digits to its left then have the significance 2exp1 = 2, 2exp2 = 4, 2exp3 = 8, and so on. For example, the binary number 1001 0101 corresponds to the decimal value 149. With these 8 digits, i.e. one byte, the numbers 0 to 255 can be represented.

Examples for the conversion of decimal numbers into binary numbers

Examples for the conversion of decimal numbers into binary numbers

Number systems make use of a number pool. In the 10-digit system (n = 10), these are the digit symbols from 0 to n-1, i.e. 0 to 9, in the 2-digit system 0 and 1.

However, there are other number systems that play a role in data processing. These are the now obsolete octal system with the digits 0 to 7 and the hexadecimal system (actually sedecimal system), which reaches up to 15, for which the decimal system does not provide enough number symbols, so that the first six letters of the alphabet A to F have to be used for the numbers 10 to 15. Both number systems, octal and hexadecimal, were introduced to make it easier for people to deal with binary numbers. The number 255, which is 1111 1111 in binary, is the letter combination FF in the hexadecimal system.

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Englisch: number system
Updated at: 13.02.2019
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