Number Systems; Computer Science
Published By Manyara on 2012-09-29 124 Views
In computer science a number system is a format in which data is numerically represented at hardware level in a computer. The three things that characterize a number system are the number of independent digits in the number systems, the place value of these digits and the maximum number that can be written with the digits provided in the number system.
There are four basic number formats/ systems namely; hexadecimal, octal, decimal and binary number systems. The difference between the number systems is essentially their bases or radix. The radix or base refers to the number of independent digits that can be used in the system. Below is an overview of these four number systems.
Decimal Number System
In decimal number system, there are ten independent digits that can be written. This means that the decimal system has a radix or base of 10. This is the number system that everyone is very familiar with. The independent digits in octal system are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0.
The reason we say that the decimal number system has 10 independent digits is that any number larger than 9 is a combination of these ten digits stated above. The next ten digits after 9 are 10 to 19 which combinations of the ten independent numbers are. This goes on to 99 and then we add an extra digit to the numbers.
Place values of decimal numbers in integer part from the decimal point are 100, 101, 102 and so on while for the fraction part they are 10-1, 10-2, 10-3 and so on.
Octal Number System
Octal number system has a base of 8 and thus eight distinct digits which are 0, 1, 2, 3, 4, 5, 6 and 7. The next digit after 7 is 10 and goes to 17 and then 20 to 27.The sequence goes on until 77 is reached and after 77 the sequence proceeds to 100 and after 777 goes to 1000. In simple terms, octal number system does not have 8 and 9 and goes to the next place value after every 7 is reached.
Place values of octal numbers in integer part are 80, 81, 82 and so on while for the fraction part they are 8-1, 8-2, 8-3 and so on.
Hexadecimal Number system
Hexadecimal number system has a radix of 16. This means that it has 16 distinct digits. It runs from 0 up to 9 but after 9 it uses A, B, C, D, E, F and G. The letters after digit 9 were used for the obvious reason of attaining the required number of distinct digits for the system.
The distinct digits of the hexadecimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F and G.
Hexadecimal number system provided a condensed method of representing large numbers in computers.
Binary Number System
A binary number system has a radix or base of 2 meaning it has only two distinct digits 0 and 1. To show how the binary numbers larger than one are got here are the first 16 numbers in the binary number system would be 0, 1, 10, 11, 100, 101, 110,111, 1000, 1001, 1010, 1011, 1100, 1101, 1110 and 1111.
Place values of binary numbers in integer part are 20, 21, 22 and so on while for the fraction part they are 2-1, 2-2, 2-3 and so on.