Number System

Hexadecimal system

b=16                         {value of A=10, B=11, C=12, D=13, E=14, F=15}

(A0F) 16

= A * 162 + 0 *161 + F *160

= 10 * 162 + 0 *161 + 15 *160

=2560 + 15

= (2575) 10

Similarly 11.116 = 1 x (161) + 1 x (160) + 1 x (16-1) = 17.062510

 12.316 = 1 x (161) + 2 x (160) + 3 x (16-1) = 18.187510

The weights of the corresponding bits for hexadecimal system are as

164163162161160.16-116-2
655364096256161.0.1250.015625
MSB    Decimal point  

Corresponding equivalents of decimal 0-15 in Binary, octal & hexadecimal system

Decimal                                Binary                   Octal                      Hexadecimal     

 0                             0000                      00                           0

 1                              0001                      01                           1           

 2                             0010                      02                           2    

 3                             0011                      03                           3 

 4                             0100                      04                           4             

 5                             0101                      05                           5     

 6                             0110                      06                           6        

 7                             0111                      07                           7                       

 8                             1000                      10                           8             

 9              1001                      11                           9                

10                           1010                      12                           A                      

11                           1011                      13                           B 

12                           1100                      14                           C                                  

13                            1101                      15                           D                         

14                            1110                      16                           E               

15               1111                      17                           F        

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