Wednesday 10 September 2014

Class on 10-09-2014 ( CSE -A & B)


 Binary to any base (Radix) conversion:
1.      Binary to decimal number conversion                 * * * * * * * * * * * * * * * * * * * * *
Ex(1): Convert  (11111)2 to decimal
Sol:  The equivalent decimal number is
                  = 1x24 + 1x23 + 1x22 + 1x21 + 1x20
                  = 16+8+4+2+1             = (31)10
Ex(2): Convert decimal equivalent of the number 10101
Sol:  The equivalent decimal number is
=  1x24 + 0x23 + 1x22 + 0x21 + 1x20
                  = 16+4+1
                  = (21)10
Ex(3): Find the decimal equivalent of the binary number (110101)
Sol:  The equivalent decimal number is
                  = 1x25 +1x24 + 0x23 + 1x22 + 0x21 + 1x20
                                    =32+16+4+1
                  = (53)10
Ex(4):  Convert (101101)2 to decimal
Sol:   The equivalent decimal number is
                  =1x25 + 0x24 + 1x23 + 1x22 + 0x21 + 1x20
                                    =32+8+4+1  = (45)10
Ex(5): Determine the decimal number of the following binary number
             (101101.10101)
Sol:      The equivalent Decimal number is
             = 1x25+0x24+1x23+1x22+0x21+1x20. 1x2-1+0x2-2+1x2-3+0x2-4+1x2-5
             = 32 + 8 +4 +1 + (1/2) + (1/8) + (1/32)
             = (45.65625)10
 Ex(6): Convert decimal equivalent of the number (0.1011)
         Sol:      The equivalent Decimal number is
                    = 1x2-1+0x2-2+1x2-3+1x2-3+1x2-4
                    = (1/2) + 0 + (1/8) + (1/16)
                    = (0.6875)10                  
      Ex (7): convert 1101110.011 to decimal
       Sol: 
                =1x26  + 1x2+ 0x24 + 1x23 + 1x22 + 1x21 +0x20 .0x2-1 + 1x2-2 + 1x2-3
                = 64+32+0+8+4+2+0.0+1/4+1/8
                = (110.375)10
       Ex (8): (1001.0101)2  to decimal form
       Sol:  
                       = 1x23 + 0x2+ 0x21 + 1x20 .0x2-1 + 1x2-2 + 0x2-3 + 0x2-4
                      =    8+0+0+1.0+1/4+0+1/16
              = (9.3125)10

2.      Binary to Octal number conversion                          * * * * * * * * * * * * * * * * * * * *

Ex 1 : convert the 1010110 to  octal number
Sol :  given number
           001|  010 | 110
           1          2        6
     Thus (1010110)2 = (126)8
Ex 2: 1110001 to octal number
Sol:   given number
            001|110|001
            1        6       1
     Thus (1110001)2=(161)8
Ex 3: 0001101 to octal number
Sol:   given number
            000|001|101
              0       1      5
       Thus   (0001101)2 = (15)8

3.      Binary to Hexadecimal number conversion                        * * * * * * * * * * * * * * * *
Ex 1:  (101011)2 to hexa decimal
Sol:    0010|1011
               2         B
        Thus (101011)2 =(2B)16
Ex 2: (1101110)2 to hexa decimal
Sol:   0110|1110
            6        E
         Thus (1101110)2 =(6E)16
Ex 3: (1010101)2 to hexa decimal
Sol:   101|0101
            6       5
        Thus (1010101)2=(65)16
Ex 4: (11101010)2 to hexa decimal
Sol:   1110|1010
            E        A
         Thus (11101010)2 = (EA)16

Octal to any base (Radix) conversion:
1.Octal to decimal number conversion                         * * * * * * * * * * * * * * * * * * * * * *
Ex 1) (152)8 to (   )10
Sol:-   =82x1 +81x5 +80x2
          =64+40+2
          =(106)10

Ex 2) (1054)8    to      (       )10
Sol:-    =83x1 + 82x0 + 81x5 + 80x4
         = 512+0+40+4
         =(556)10

Ex 3) convert  (6327.4051)8 in to its equivalent decimal number
Sol:- = (6x83 + 3x82 + 2x81 + 7x80) . (4x8-1 + 0x8-2 + 5x8-3 +1x8-4)
            = (3072+192+16+7) . (4/8+0+5/512+1/4096)
        = (3287.5100098)10

Ex 4) convert  (4057.06)8 in to its equivalent decimal number
Sol:- =4x83 +0x82 + 5x81 + 7x80 . 0x8-1 + 6x 8-2  
         =(2048 + 0 + 40 + 7) . (0 + 0.0937)
         =(2095 .0937)10
1.      Octal to binary number conversion                                 * * * * * * * * * * * * * * * * * *

Ex 1) convert (721)8 to binary number
Sol:- Given number        7       2         1
                                     (111)   (010)   (001)
So, therefore (721)8 = (111010001)2
Ex 2) convert (1263)8 to binary number
Sol:- Given number  
  1             2           6               3
(001)     (010)   (110)        (011)
So, therefore (1263)8=(001010110011)2
Ex 3) convert (425)8 to binary number
Sol:- Given number
    4             2          5
(100)      (010)    (101)
So,  therefore (425)8 =(100010101)2
Ex 4) (71)8 to binary number
Sol:-  Given number  
    7            1
(111)      (001)
So, therefore (71)8=(111001)2

2.    1.      Octal to Hexadecimal number conversion                     * * * * * * * * * * * * * * * * * *

     Ex.1)  (467)8 to (___)16
     
           4         6          7
        Here, we have to write the each digit in 3-bit binary form.

       Now divide the values with 4 digits, from right to left
       
                                                      Thus  (467)8  =  (137)16
      Ex.2)  (761)8 to (___)16


                      7            6              1
               Here, we have to write the each digit in 3-bit binary form.
  
          Now divide the values with 4 digits, from right to left

              


         Ex.3)  (6531)8 to (___)16

                   6         5         3         1
         Here, we have to write the each digit in 3-bit binary form.

          
 Now divide the values with 4 digits, from right to left

       


     
Thus  (6531)8 =  (D59)16







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