The following examples are related to the work covered in WEEK 18.

• (a) AD13 HEXADECIMAL to DECIMAL.
  
  

                                       0
                    Place values are 16  = 1 decimal 
                                       1
                                     16  = 16 decimal
                                       2
                                     16  = 16 x 16 = 256 decimal
                                       3
                                     16  = 16 x 16 x 16 = 4096 decimal
                    

  So AD13 = A x 4096 + D x 256 + 1 x 16 + 3 x 1
  
  Remember that A = 10 decimal and D = 13 decimal, so final calculation is:-
  
  10 x 4096 + 13 x 256 + 1 x 16 + 3 x 1 = 40960 + 3328 + 16 + 3 = 44,307
  
  
• (b) AD1C HEXADECIMAL to BINARY.
  
  

                    4 bit binary values are A = 1010
                                            D = 1101
                                            1 = 0001
                                            C = 1100
                    

  
  So binary value is 1010 1101 0001 1100
  
  
• (c) 0111011 BINARY to HEXADECIMAL.
  
  Split binary value into 4 digit groups starting from the right hand side.
  
  011 1011, now add any zeroes needed to make left group up to 4 digits
  
  0011 1011, now convert each group to hexadecimal.
  
  0011 = 3 and 1011 = B so hexadecimal value is 3B
  
  
• (d) 1001110 BINARY to DECIMAL.
  

                                      0
                    Place values are 2  = 1 decimal
                                      1
                                     2  = 2    "
                                      2
                                     2  = 4    "
                                      3
                                     2  = 8    "
                                      4
                                     2  = 16   "
                                      5
                                     2  = 32   "
                                      6
                                     2  = 64   "
                    

  So decimal value is 1 x 64 + 0 x 32 + 0 x 16 + 1 x 8 + 1 x 4 + 1 x 2 + 1 x 1 which is
  64 + 8 + 4 + 2 = 78 decimal