Decimal to any base conversion & Hexa to any base conversion (Class on 11-09-14 for CSE-A &B)

Decimal to any base (Radix) conversion:

1.      Decimal to binary number conversion                         * * * * * * * * * * * * * * * * * *

Take the remainders from bottom to top,

The result of 57₁₀ is =(111001)₂

Ex:2 Convert 0.75₁₀to binary

            Multiply the given fraction by 2.

Keep the integer in the product as it is and multiply the new fraction in the product by 2. Continue this process & read the integers in the products from the top to bottom.

             

                 Given fraction                    0.75

            Multiply 0.75 by 2                  1.50

            Multiply 0.50 by 2                  1.00

Reducing the integers from top to bottom (0.75)₁₀=(0.11)₂

Ex (3): Convert (105.15)₁₀ to binary.

Sol:      Conversion of integer 105

Remainder from bottom to Top = 1101001   

This particular fraction can never be expressed exactly in binary. This process may be terminated after few steps.

                        Therefore (105.15)₁₀= (1101001.001001)₂

Ex (4): Convert (13)₁₀ to an equivalent base-2 number.

Ex (5): Convert (0.65625)₁₀ to an equivalent base-2 number.

1.      Decimal to Octal number conversion                         * * * * * * * * * * * * * * * * * * *

  Ex (1): (574)₁₀  

                                            Thus  (574)₁₀  = (1076)₈

Ex (2): (247)₁₀  

Ex (3): Convert (0.6875)₁₀ into Octal number.

Ex (4): Convert (3287.5100098)₁₀  into Octal number.

Fractional Part 0.5100098

1.      Decimal to Hexadecimal number conversion                         * * * * * * * * * * * * * * *

Ex (1):    (95.5)₁₀

Ex (2):    (675.625)₁₀

Hexa decimal to any base (Radix) conversion:

1.      Hexadecimal to binary number conversion                                * * * * * * * * * * * * *

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

Ex 1:convert (A72E)₁₆ to octal number

                    A      7       2       E

   

     1010  0111 0010 1110

  = 001 010 011 100 101 110

        1     2     3    4     5    6

   = (123456)₈

Ex 2: Convert (0.BF85)₁₆ to octal number

            0.1011111110000101

           

            0.101|111|111|000|010|100

           

           0.   5    7     7    0      2    4

Thus (0.BF85)₁₆=(0.577024)₈

Ex 3: Convert B9F.AE₁₆ to octal

Given hex number is              B        9        F       .    A           E

Convert hex digit to binary  1011  1001   1111   .  1010     1110

Groups of three bits are                   101 110 011 111. 101 011 100

Convert each 3 bit group to octal      5     6      3     7   .   5      3      4

           

The result is (5637.534)₈

Ex 4: (2AB)₁₆ -------(  )₈

             

Ex 5: (42FD)₁₆--------(   )₈

                

          =   4        2         F        D

            0100   0010  1111  1101

            

          = 000|100|001|011|111|101

            

              0      4     1    3      7    5

Thus (42FD)₁₆=(41375)₈

2.      Hexadecimal to decimal number conversion                                * * * * * * * * * * * * *

Ex 1: convert 5C7₁₆ to decimal

            =(5x16²)+(12x16¹)+(7x16⁰)

            =1280+192+7             

            =(1479)₁₀

Ex 2: convert A0FP.0EB₁₆ to decimal

            =(10x16³)+(0+16²)+(15x16¹)+(9x16⁰).(0x16^-1)+(14x16^-2)+(11x16^-3)

            =(40960+0+240+9)+(0+0.0546+0.0026)

            =(41209.0572)₁₀

Ex 3: convert AB6 to decimal

            =10x16²+11x16¹+6x16⁰

             =(2742)₁₀

Ex 4: convert 2EB7 to decimal

            =2x16³+14x16²+11x16¹+7x16⁰            

            =(11959)₁₀

Ex 5: convert A08F.EA to decimal

            =(10x16³+0x16²+8x16¹+15x16^{0 )} + (14x16^-1+11x16^-2)

            =(41103.0.917)₁₀

Ex 6: (8E47.AB)₁₆------(   )₁₀

            =(8x16³+14x16²+4x16¹+7x16^{0 )} + (10x16^-1+11x16^-2)

            =(36423.667)₁₀

Ex 7: obtain decimal equivalent of hexadecimal(3A.2F)₁₆

            =(3x16¹+10x16⁰⁾  + (2x16^-1+15x16^-2)

            =48+10+(2/16)+(15/16²)

            =(58.1836)₁₀

Attendance on 11-09-14 (CSE-A)

Attendance on 11-09-14  (CSE-A)

Absentees: 6, 8, 33, 42 ,43, 45 ,52, 58

Attendance on 11-09-2014 (CSE-B)

Attendance on 11-09-2014 (CSE-B)

DLD lab

Total Strength : (561-590)

Absentees: 63, 67, 72, 73, 74, 77, 79, 81, 89

Topic : Introduction to DLD lab


Class:

Absentees: 63, 67, 71, 72, 74, 79, 91, A3, A4, B4, B8, B9 

Topics:  (1).Octal to any base conversion
              (2). Hexa to any base conversion

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  + 1x2⁵  + 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 + 0x2²  + 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

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

Attendance on 10-09-2014  CSE-A class

Absentees: 2,36,8,25,27,31,42,43,45,48,50,52


Attendance on 10-09-2014  CSE-A  DLD Lab

Attended:  (501-560)
Absentees: 2,36,8,25,27,31,42,43,45,48,50,52 

Attendance on 10-09-2014  CSE-B               

Absentees: 74, 79, 84, 85, 91, A4, B3, B4, B9   

Attendance on 09-09-2014 (CSE-A & B)

 Attendance on 09-09-2014 CSE-A

Total Strength: (501-560)

Absentees :  1,5,6,7,8,9,10,11,13,15,19,21,25,26,27,30,31,36,37,40,41,42,43,45,46,48,50,52,55,56,58


 Attendance on 09-09-2014 CSE-B

Total Strength: (561-5C0)

DLD Lab: (591-5C0)

Absentees : 
91,96, A1, A2, A3, A8, A9, B1, B8, B9

Attendance on 08-09-2014 (CSE-B)

CSE-B Attendance on 08-09-2014

Total Strength = 60 members (561 to 5C0)
Today Absentees = 61,65,74,75,78,79,80,81,82,84,89,92,95,96,A2,A3,A4,A5,A8,A9,B2,B4,B8,B9
Today total absentees = 24 members.

Today topics :
Introduction - Number systems - Number systems Conversion -  Binary to decimal number conversion

Number System Conversion - Binary to any base (Radix) conversion:

NUMBER SYSTEMS CONVERSION:

Binary to any base (Radix) conversion:

1.      Binary to decimal number conversion

2.      Binary to Octal number conversion

3.      Binary to Hexadecimal number conversion

Octal to any base (Radix) conversion:

1.      Octal to decimal number conversion

2.      Octal to binary number conversion

3.      Octal to Hexadecimal number conversion

Decimal to any base (Radix) conversion:

1.      Decimal to binary number conversion

2.      Decimal to Octal number conversion

3.      Decimal to Hexadecimal conversion

Hexa decimal to any base (Radix) conversion:

                       1.   Hexadecimal to binary number conversion

                       2.      Hexadecimal to Octal number conversion

                       3.      Hexadecimal to decimal number conversion

 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  + 1x2⁵  + 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 + 0x2²  + 0x2¹ + 1x2⁰ .0x2^-1 + 1x2^-2 + 0x2^-3 + 0x2^-4

                      =    8+0+0+1.0+1/4+0+1/16

              = (9.3125)₁₀