# Number Systems Used on Computers: Decimal, Binary, Octal and Hexadecimal (Especially for GATE-Geospatial 2022)

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Number systems are the technique to represent numbers in the computer system architecture, every value that you are saving or getting into/from computer memory has a defined number system.

Digital computer system stores information represented by the digits of number system. **Binary number system** is used as a representation of information inside the computer. However, due to the lower radix value of the binary system, it is not efficient for presentation of information. Hence, outside computers other number systems are used.

The use of **decimal number system** for this purpose would have been most natural, as it is widely used all over the world. However, the representation of the 10 digits of the decimal number system requires some device which can assume 10 discrete states. Therefore, the decimal number system cannot be used as the internal representation of the information in decimal computers.

The only number system whose digits can be easily represented with devices like communicates (solid states) vacuum tubes, transistors, etc. is the binary system. The digits of this number system are 0 and 1.

All type of data stored in a computer as binary number consisting of **bi**nary digi**t**s (bit) . The value that may be taken by either 0 or 1, and can represent only two states – OFF and ON.

The **octal number system**, having base eight digits from 0,1, 2 to 7, and **hexadecimal number system** , having base 16 and 16 digits from 0,1, 2 to 9 and A, B, C, D, E and F are used for representation of information external to the computer. The digits A to F have the equivalent decimal values 10, 11, 12,13, 14 and 15 respectively.

Different number system used either internal or external representation of information in digital computers.