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Number System


           In our everyday lives, we use the decimal numbering system. These are digits 0 through 9. Every number expressed in the decimal system is a combination of these ten digits i.e. 360, 418, 086 etc. These numbers uses only digits 0 through 9. However, there is another system which is used in computers, called binary system.


                The binary system works in essentially the same way, with the only difference being that it only has two digits. These are visually expressed by the digits 0 and 1, and every number expressed in the binary system is a combination of 0 and 1.

                These numbers (0 and 1) are actually a representation of signals. In modern electronic technology, computer circuit has only two states, on or off. 0 represent off while 1 represent on. There are many other Number Systems i.e. Octal Number System, Decimal Number System, Hexadecimal Number System etc.

Decimal Number System – In above discussion, we saw that it uses numbers through 0 to 9, let’s understand with an example.

Ex – Suppose a number is 7549, this number can be represent as 7 thousand 5 hundred forty nine or can be written as

7000 + 500 + 40 + 9 or

(7*103) + (5*102) + (4*101) + (9*100)

In this sequence, we can easily see that there is an increasing power of 10 with corresponding digit from right to left. Remember this I’m focusing from right to left. The decimal number system is said to be of base, or radix, 10 because it uses 10 digits. Similarly Binary Number system has only two digits, so the base or radix of binary number system is 2. Let us take an example of binary number.

Ex – 110010

This number can be written as above example only change is that 10 is replace by 2 because the base of this system is 2.

(1*25) + (1*24) + (0*23)  + ( 0*22) + (1*21) + (0 *20)

 

Note: We can write our custom number system with required base. Let’s take some examples of different bases.

Ex 1.Number = 432 and base = 5

Sol. (4*52) + (3*51) + (2*50)

Ex 2. Number = 542 and base = 6

Sol. (5*62) + (4*61) + (2*60)

 

Note: Suppose a number system of base n than it consists only n-1 digits because every number system starts with 0. In above Ex 1. Here is a base 5 and use only 0 to 4 digits (432) not more than or equal to 5, In Ex 2. Here is a base 6 and use only 0 to 5 digits (542) not more than or equal to 6

In our next article , we will discuss some important number system.




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