Can Anyone Explain Different Number Systems?

Humans are very curious and always in search of best solutions. For counting things different number systems are used. Some of them are Decimal number system, Binary number system, Hexadecimal system and octal number system. Every number system has a base called Radix. In decimal number system basic numerals are ten; these are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Decimal number system is used in mathematics, accounts and some other subjects. Most commonly number system use in daily life is decimal number system.

A computer works with electricity and have only two conditions that either current is On or current is OFF. So most comely used number system in computers is binary number system. It consist of only two values 0 and 1. 0 means OFF and 1 means On. The Radix of Octal number system is 8. Octal number system consist of eight numeric values; 0, 1, 2, 3, 4, 5, 6 and 7. The Radix of Hexadecimal number system is 16. Decimal number system consist of sixteen numeric values; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D and E.

Computer system uses four numbering systems, binary, octal and hexadecimal. Each has advantages for different levels of digital processing. Within a number, each symbol is called a digit (decimal digit, binary digit, octal digit and hexadecimal digit). For example the decimal number 769 has three decimal digits. Digits are arranged in order of ascending value, moving from the lowest value on the right to the highest on the left. For this reason the left most digits referred to as most significant and the rightmost as the least significant digit. For instance; in the decimal number 3456, the most significant digit is the 3, and the least significant is the 6.
The decimal number system is the one most familiar to us in our everyday life. All our terms for indicating countable quantities are based on it, and in fact when we speak of other numbering systems, we tend to refer to their quantities by their decimal equivalents.
The binary number system provides the basis for all computer operations. Computers work by manipulating electric current on and off. The binary system uses two symbols, 0 and 1, so it corresponds naturally to a two-state device, like a switch with 0 to represent the off and 1 represent the on sate.
The octal number system is used by computer programmers to represent binary numbers in compact form.
Hexadecimal number system is base 16. Like octal number system it is used by programmers to represent binary numbers in compact form.

The number systems are basically categorized into two types:

1) Non Positional Number systems
2) Positional Number systems

Non Positional Number System: In early ages, fingers were used for counting; when ten fingers were not enough then stones, sticks or pebbles were used. This approach uses additive techniques, symbols such as I for 1, II for 2, III for 3, IIII for 4, IIIII for 5 etc. Each symbol represented the same value regardless of its position in the number and the symbols were added to find out the value of the number. This system was inadequate and was very difficult to perform even simple arithmetic thus the Positional Number System was designed as time passes.

Positional Number System: In the Positional Number system there are few symbols called digits and the digits represent different values depending on their position in the number. The value of each digit is determined by three conditions.

• The digit itself.
• Position of the digit in the number.
• The base of the number system where the base means the total number of digits in the number system.

For example, We use Decimal number system in our day to day life and the base of Decimal number is system is 10 as there are 10 digits (0,1,2,3,4,5,6,7,8,9).

The other Positional Number Systems are:

1) Binary Number System
2) Octal Number System
3) Hexa-Decimal Number System

Explain binary addition