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Conversion of a hexadecimal number to a binary
                    number

METHOD 1

       First it should be converted to its equivalent
        decimal number

       Then convert the decimal number so obtained
        to its binary equivalent


                    http://improvec.blogspot.in/         1
METHOD 2

Each digit of the given hexadecimal number should be
       converted to its 4-bit binary equivalent




                    http://improvec.blogspot.in/       2
1.Convert the hexadecimal number ABC to its
          equivalent binary number


 METHOD 1

     (ABC)16 = A *162 + B*161 + C*160
            = 10 *256 + 11*16 + 12*1
            = 2560 + 176 + 12
            = (2748)10
          (1010 1011 1100)10

                   http://improvec.blogspot.in/   3
Now converting this decimal into binary
    Division        Remainders
    2 2748
    2 1374 0
    2 687           0
    2 343           1
    2 171           1
    2 85            1
    2 42            1
    2 21            0
    2 10            1
    2 5             0
    2 2             1
    2 1             0
    2 0             1
Thus (ABC)16 = (2748)10 = (101010111100)
                        http://improvec.blogspot.in/   4
METHOD 2

A16 = (10)10 = (1010)2         2 10
B16 = (11)10 = (1011)2         2 5 0
C16 = (12)10 = (1100)2          2 2 1
                                   2 1 0
                                       0 1
                            (10)10 = (1010)2

(ABC)16 = ( 1010 1011 1100 )2

                    http://improvec.blogspot.in/   5
2. Convert the hexadecimal number 6B9 to its
           equivalent binary number
 Each digit of the given hexadecimal number is
  converted to its 4-bit binary equivalent

      (6B9)16 = (0110) (1011)(1001)
              = (011010111001)2
              = (011010111001)2




                     http://improvec.blogspot.in/   6
3. Convert the hexadecimal number 6D.3A to its
           equivalent binary number
 Each digit of the given hexadecimal number is
  converted to its 4-bit binary equivalent

      (6D.3A)16 = (0110) (1101) . (0011) (1010)
                =(01101101.00111010)2
                =(1101101.0011101)2




                    http://improvec.blogspot.in/   7
Summary

In this class, you have learnt about



 Conversions of binary number to hexadecimal

 Conversions of hexadecimal to binary number




                      http://improvec.blogspot.in/   8
Frequently Asked Questions


 Explain how to convert a binary number to
  equivalent hexadecimal

 Explain how to convert a hexa decimal number to
  equivalent binary




                    http://improvec.blogspot.in/    9
Quiz

 The binary equivalent of (ABC)
  a. 1010 1011 1100
  b.1010 1100 1100
  c. 1011 1010 1101
Answer: a




                     http://improvec.blogspot.in/   10

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Hexa to binary

  • 1. Conversion of a hexadecimal number to a binary number METHOD 1 First it should be converted to its equivalent decimal number Then convert the decimal number so obtained to its binary equivalent http://improvec.blogspot.in/ 1
  • 2. METHOD 2 Each digit of the given hexadecimal number should be converted to its 4-bit binary equivalent http://improvec.blogspot.in/ 2
  • 3. 1.Convert the hexadecimal number ABC to its equivalent binary number  METHOD 1 (ABC)16 = A *162 + B*161 + C*160 = 10 *256 + 11*16 + 12*1 = 2560 + 176 + 12 = (2748)10 (1010 1011 1100)10 http://improvec.blogspot.in/ 3
  • 4. Now converting this decimal into binary Division Remainders 2 2748 2 1374 0 2 687 0 2 343 1 2 171 1 2 85 1 2 42 1 2 21 0 2 10 1 2 5 0 2 2 1 2 1 0 2 0 1 Thus (ABC)16 = (2748)10 = (101010111100) http://improvec.blogspot.in/ 4
  • 5. METHOD 2 A16 = (10)10 = (1010)2 2 10 B16 = (11)10 = (1011)2 2 5 0 C16 = (12)10 = (1100)2 2 2 1 2 1 0 0 1 (10)10 = (1010)2 (ABC)16 = ( 1010 1011 1100 )2 http://improvec.blogspot.in/ 5
  • 6. 2. Convert the hexadecimal number 6B9 to its equivalent binary number  Each digit of the given hexadecimal number is converted to its 4-bit binary equivalent (6B9)16 = (0110) (1011)(1001) = (011010111001)2 = (011010111001)2 http://improvec.blogspot.in/ 6
  • 7. 3. Convert the hexadecimal number 6D.3A to its equivalent binary number  Each digit of the given hexadecimal number is converted to its 4-bit binary equivalent (6D.3A)16 = (0110) (1101) . (0011) (1010) =(01101101.00111010)2 =(1101101.0011101)2 http://improvec.blogspot.in/ 7
  • 8. Summary In this class, you have learnt about  Conversions of binary number to hexadecimal  Conversions of hexadecimal to binary number http://improvec.blogspot.in/ 8
  • 9. Frequently Asked Questions  Explain how to convert a binary number to equivalent hexadecimal  Explain how to convert a hexa decimal number to equivalent binary http://improvec.blogspot.in/ 9
  • 10. Quiz  The binary equivalent of (ABC) a. 1010 1011 1100 b.1010 1100 1100 c. 1011 1010 1101 Answer: a http://improvec.blogspot.in/ 10