Question

Convert 3BA.25 (base 14) to base 6 ? Show all arithmetic in decimal

Answer 1

Answer:

$(3252.1001)_{6}$

Explanation:

• To convert the base 14 to base 10 :

$(3BA.25)_{14}$= $3*14^{2}$ + $B*14^{2}$ + $A*14^{0}$ + $2*14^{-1}$ + $5*14^{-1}$

Then,    = $588+154+10+\frac{2}{14^{1}} + \frac{5}{14^{2}}$

Then,    =$752 + 0.168$

            =$(752.168)_{10}$

• To convert base-10, [text](752.168)_{10}[/text] to base 6.

     6 | 752 | 2

     6 | 125 | 2

     6 | 20  | 2

     6 | 3    | 3

        | 0    |

Then, the conversion part 752 which has base-6 = 3252

• Then, the conversation of the decimal part .168 to base 6

$0.168*6=1.008$ and the integer part is 1.

$0.008*6=0.048$ and the integer part is 0.

$0.048*6=0.288$ and the integer part is 0.

$0.288*6=1.728$ and the integer part is 1.

Then, the conversion of decimal part is $(0.1001)_{6}$

Finally, the answer is  $(3252.1001)_{6}$