Convert 473 to base 3

Question

b) Convert FD3 to base ten

 

e) Convert 101110001 to decimal

Answer 1

a)

       473/3     is     157  remainder 2

       157/3     is      52  remainder 1

       52/3      is       17  remainder 1

       17/3     is      5  remainder 2

        5/3      is      1 remainder 2

        1/3      is      0  remainder 1

Reading the remainders in reverse order:

     473₁₀ = 122112₃

 

b)  [note: I assume FD3 is hexadecimal]

               3             [units]

            208            [D=13, so 13*16]

          3840            [F=15, so 15*16*16]

         -------

          5051₁₀           [base 10 is decimal]

 

c)

    

  2⁸   2⁷   2⁶   2⁵   2⁴   2³  2²  2¹  2⁰

  1    0    1    1     1    0   0   0    1

 

  256

    64

    32

    16

      1

---------

  369

 

Using the easy conversion of 1 0111 0001₂ = 171₁₆

   it is often easier to convert binary to hexadecimal, then convert hexadecimal to decimal.

Answer 2

b) this is an hexadecimal number = 15(16²) + 13(16) + 3

 

c) this appears to be a BINARY number; if that's correct, for each one in position i, with i running from 0 for the rightmost bit, and increasing by 1 for each leftward movement, compute the sum of 2ⁱ; note that there is no contribution from positions i where the bit is zero.  In other words, the decimal equivalent is the sum of SOME powers of two.

 

I letting you do the work, assuming that you can learn from these principles.