Number system

             Number system

Ø Positional number system

In a positional number system, there are only a few symbols called digits. These symbols represent different values, depending on the position they occupy in a number. The value of each digit in such a number is determined by three consideration:

1.    The digit itself

2.    The position of the digit in the number, and

3.    The base of the number system (where base is defined as the total number of digits available in the number system).

§  Binary number system

Binary number system, in mathematics, positional numeral system employing 2 as the base and so requiring only two different symbols for its digits, 0 and 1, instead of the usual 10 different symbols needed in the decimal system. The numbers from 0 to 10 are thus in binary 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, and 1010. The importance of the binary system to information theory and computer technology derives mainly from the compact and reliable manner in which 0s and 1s can be represented in electromechanical devices with two states—such as “on-off,” “open-closed,” or “go–no go.”

§  Octal number system

Octal Number System is one the type of Number Representation techniques, in which there value of base is 8. That means there are only 8 symbols or possible digit values, there are 0, 1, 2, 3, 4, 5, 6, 7. It requires only 3 bits to represent value of any digit. Octal numbers are indicated by the addition of either an 0o prefix or an 8 suffix.

Position of every digit has a weight which is a power of 8. Each position in the Octal system is 8 times more significant than the previous position, that means numeric value of an octal number is determined by multiplying each digit of the number by the value of the position in which the digit appears and then adding the products. So, it is also a positional (or weighted) number system.

§  Decimal number system

If the Base value of a number system is 10, then it is called Decimal number system which has most important role in the development of science and technology. This is the weighted (or positional) number representation, where value of each digit is determined by its position (or their weight) in a number. This is also known as base-10 number system which has 10 symbols, these are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Position of every digit has a weight which is a power of 10. Each position in the decimal system is 10 times more significant than the previous position, that means numeric value of a decimal number is determined by multiplying each digit of the number by the value of the position in which the digit appears and then adding the products.

§  Hexadecimal number system

Hexadecimal Number System is one the type of Number Representation techniques, in which there value of base is 16. That means there are only 16 symbols or possible digit values, there are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Where A, B, C, D, E and F are single bit representations of decimal value 10, 11, 12, 13, 14 and 15 respectively. It requires only 4 bits to represent value of any digit. Hexadecimal numbers are indicated by the addition of either an 0x prefix or an h suffix.

Position of every digit has a weight which is a power of 16. Each position in the Hexadecimal system is 16 times more significant than the previous position, that means numeric value of an hexadecimal number is determined by multiplying each digit of the number by the value of the position in which the digit appears and then adding the products. So, it is also a positional (or weighted) number system.

Ø Non positional number system

In this system, we have symbols such as Ī for 1, ĪĪ for 2, ĪĪĪ for 3, etc. Each symbol represents the same value regardless of its position in a number, and to find the value of a number, one has to count the number of symbols present in the number. Since it is very difficult to perform arithmetic with such a number system, positional number system were developed.