Perfect Computer Notes

Super Easy Short Computer Notes To Improve Computer Literacy and Your IT Skills

Sponsored Links

Saturday, June 1, 2019

Number Systems in Computer Science and Conversion Method

By DecentChoice: Admin 7:30 AM Leave a Comment

Q1. What is a Number System? What are different types of number system?

Number system

A number system is a set of digits, symbols and rules to express quantities in counting and calculations. Following are the most commonly used number systems:


Number-systems-in-computer-science-easy-conversion-methods-with-pictures
Number-systems-in-computer-science-easy-conversion-methods-with-pictures

Decimal Number System

It is most commonly used number system. It has 10 symbols{0,1,2,3,4,5,6,7,8,9}. It is also called base 10 number system. People normally use decimal number system to represent numbers.


Binary Number System

In binary number system there are only two symbols {0 and 1}. In a computer all data is represented by Binary number system. This is because computer’s electronic switches have only two states on and OFF. When a switch is ON it represents a 1 and when a switch is OFF, it represents a Zero.

Octal Number System

Octal number system consists of 8 digits{0,1,2,3,4,5,6,7}. Its base is 8. It is used as shorthand for long binary numbers. Each octal digit represents 3 binary digits.

Octal
Binary
0
000
1
001
2
010
3
011
4
100
5
101
6
110
7
111


Hexadecimal Number System

Hexadecimal number system is used to represent long binary numbers in an easy and short form. Its base is 16. It has sixteen symbols{0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}. Each hexadecimal digit represents 4 binary digits.
Hexadecimal
Binary
Hexadecimal
Binary
0
0000
8
1000
1
0001
9
1001
2
0010
A
1010
3
0011
B
1011
4
0100
C
1100
5
0101
D
1101
6
0110
E
1110
7
0111
F
1111



Q2. Conversion of Decimal (Integer part) to other systems

                                  
a) 4510 = (?)2   
b) 11910 =(?)8
c) 19010 =(?)16
2
45
2
22-1
2
11-0
2
5  -1
2
2  -1
2
1  -0

0  -1 
8
119
8
14-7
8
1  -6

0  -1
16
190
16
11-14(E)

0  -11(B)
   
           

=> 4510 = (101101)2                          4510=(167)8                       19010=(BE)16                       


Q3. Conversion of Decimal system (Fraction part) to other systems

a) (.23)10   = (?)2
b) (.225)10 = (?)8
c) (.225)10 = (?)16
Fraction
Integer
.23 X 2 = 0.46
.46
0
.46 X 2 = 0.92
.92
0
.92 X 2 = 1.84
.84
1
.84 X 2 = 1.68
.68
1
.68 X 2 = 1.36
.36
1

=> (.23)10   = (.00111)2        [Similar method is used for decimal (fraction) to Octal (multiply by 8)and hexadecimal(multiply by 16)]

Q4. Conversion of Other systems (Integer part) to Decimal


a)  (101101)2    =( ? )10     b)    (167)8  = (?)10                 (BE)16 =(?)10                      
   
  a) (101101)2                                                   
     =1x25+0x24+1x23+1x22+0x21+1x20 
    = 32   + 0   +   8   +  4   + 0     +1
    = 45 
b) (167)8          
     =1x82+6x81+7x80 
    = 64   + 48   +  7
    = 119 
c) (BE)2            
     =Bx161+Ex160 
    =  11x161+14x160 
    =  176   + 14
    =   190 


Q5. Conversion of Other systems(Fraction part) to Decimal number system

a)  (.110)2    =( ? )10     b)    (.75)8  = (?)10                 (.13)16 =(?)10                       
   
  a) (.110)2                                                        
     =.{1x2-1+1x2-2+0x2-3} 
     =.{ 1/2   + 1/4   +   0}
     =.{  .5    +  .25  +    0}
     =.75
b) (.75)8            
     =.{7x8-1+5x8-2  }
     =.{ 7/8   + 5/64 }
     = .{.875 + .0781}
     = .9531 
c) (.13)16           
     =.{1x16-1+3x16-2  }
     =.{1/16   +3/256} 
    =  .{.0625   + .01171}
    =   .0742 



      Conversion of  non-decimal Number system to Other non-decimal number system


      For example to convert OCTAL into HEXADECIMAL, use the follwing steps:

1)            Convert octal into decimal

2)            Convert decimal into hexadecimal





0 comments:

Post a Comment

AddToAny

Sponsored Links
.