Skip to main content

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.




Comments

Post a Comment

Popular posts from this blog

Complement of a Number

Subtraction of Binary Numbers  ;  Octal and Hexadecimal Number  ;  Convert Decimal to Binary Complements Complements are used in digital computers for simplifying the subtraction operation and for logical manipulations. There are two types of complements for each base-r system: (1) the r’s complement and (2) the (r-1)’s complement. When the value of the base is substituted, the two types receive the names 2’s and 1’s complement for binary numbers,  10’s and 9’s complement for decimal numbers. The r’s Complement Given a positive number N in base r with an integer part of n digits, the r’s complement of N is defined as r n   - N for N is not equal to 0 and 0 for N = 0. The following numerical example will help clarify the definition. The 10’s complement of (52520) 10 is 10 5 – 52520 = 47480 The number of digits in the number is n= 5 The 10’s complement of (0.3267) 10 is 1 – 0.3267 = 0.6733 No integer part, so 10 n = 10 0 = 1 The 10’s...
Post a Comment
Read more

mathematics skills

Are you ready to give your mathematics skills a boost? These simple math tricks can help you perform calculations more quickly and easily. They also come in handy if you want to impress your teacher, parents, or friends. 01 The Answer Is 2 Think of a number. Multiply it by 3. Add 6. Divide this number by 3. Subtract the number from Step 1 from the answer in Step 4. The answer is 2. Same Three-Digit Number Think of any three-digit number in which each of the digits is the same. Examples include 333, 666, 777, and 999. Add up the digits. Divide  the three-digit number by the answer in Step 2. The answer is 37. Six Digits Become Three Take any three-digit number and write it twice to make a six-digit number. Examples include 371371 or 552552. Divide the number by 7. Divide it by 11. Divide it by 13. The order in which you do the division is unimportant! The answer is the three-digit number. Examples: 371371 gives you 371 or 552552 gives you 552. A related trick is to take any three-di...
Post a Comment
Read more

Types of Number System

Different Number Systems – There are some different Number System with correspondence base. Which will describe as follows-   Number System  Base  Representation  Binary Number System      2  (Number) 2  Decimal Number System      10  (Number) 10  Octal Number System      8  (Number) 8  Hexadecimal Number System     16   (Number) 16 Note : Any number can be in decimal form. So there is an another way to solve them quickly. Let’s understand with an example. Ex 1. (4064.10) 10   Sol. This Number can also be written as (4*10 3 ) + (0*10 2 ) + (6*10 1 ) + (4*10 0 ) + (1*10 -1 ) + (0*10 -2 ) Note that after decimal digits we will use decreasing power of 10 from left to right. Ex 2.   (1101.01) 2        Sol. This Number can also be written as (1*2 3 ) + (1*2 2 ) + (0*2 1 ) + (1*2 0 ) + (0*2 -1 ) + (0*2 -2 ) Exercise: From Ques...
Post a Comment
Read more