# binary system

The binary system is a logical number system that has 2 as its base and therefore only works with the two numbers 0 and 1. With the binary number the numbers are written in the same value order as with the decimal number: to the right the least valence, to the left the valence increases.

The value of the right digit corresponds in exponential notation to `2^0`, the preceding one to `2^1`, the next one to `2^2, 2^3 etc. 2^4`, which represents the digit with the lowest valence, is on the far right. If the digit `2^0` increases by the value 1 to `2^1`, then the value of `2^0` falls back to 0. The last digit thus always changes from 1 to 0 to 1 ... and so on. The second digit from the right changes at every second value and the third digit at every fourth value.

If decimal numbers are represented in the binary system, they are more multi-digit and much longer, because with each increase of the exponent the binary number series increases by one digit. If the digit '2^3' with which the digits between 0 and 8 can be represented consists of four binary values, then the next higher binary number '2^4' consists of five digits. For example, the decimal number 5 is represented in binary as 0101, the number 9 in binary as 1001, and the number 20 as 10100.

The binary system, also known as the dual system, forms the basis of dual arithmetic and Boolean algebra and is of fundamental importance for digital data processing: in the logical domain as the basis for binary codes and number systems, and in the technical domain as the basis for circuits and memories.

Just as with the decimal system, all basic arithmetic operations - addition, subtraction, multiplication and division - can be performed with the binary system. It is also possible to convert binary numbers directly into decimal numbers and vice versa.