Convert the numeral to a numeral in base ten. 5336 16

Question

Convert the numeral to a numeral in base ten.
5336 16

 

Answer 1

Both decimal and hexadecimal are positional number systems.  That means each digit has a place value that is a power of the number base.

 

So,  

    abc (decimal) is a*10² + b*10¹ + c*10⁰

and

   abc (hexadecimal ) is a*16¹ + b*16¹ + c*16⁰     [numbers listed as decimal]

 

5226₁₆ is

   5*16³      +    3*16²    +    3*16¹    +    6*16⁰

   20480    +    768      +     48        +    6

       21302      (in decimal)

 

You may also loop through the calculations:

    (5*16 * 3)*16 + 3)*16 + 6

       5*16=80

       80+3=83

       83*16=1328

       1328+3=1331

       1331*16=21296

       21296+6=21302

 

The most interesting method uses recursion:

        5336 (hexadecimal)

                                         (somethingA)*16 + 6    [recursive case]

                             ((somethingB]*16+3)*16 + 6    [recursive case]

                 (((somethingD)*16+3)*16+3)*16 + 6    [recursive case]

                 (((somethingE)*16+3)*16+3)*16 + 6    [recursive case]

                              ((((5)*16+3)*16+3)*16 + 6     [base case]

                                        (((83)*16+3)*16 + 6

                                                  (1331)*16 + 6

                                                         21302        (decimal)

Answer 2

Our normal counting is in base 10.

That is 1's + 10's+100's+1000's .... + a10ⁿ

 

6549=9(10⁰)+4(10¹)+5(10²)+6(10³)

 

Apply the same logic to base 16

 

5336₁₆

=6(16⁰)+3(16¹)+3(16²)+5(16³)

 

Plug those into your calculator.

 

Note : take a lok at the following site:

 

 http://gwydir.demon.co.uk/jo/numbers/binary/bases.htm