SOLUTION
Let us start with
a. To convert
[tex]0.6640625_{10}\text{ to base 2}[/tex]To do this, we keep multipllying by 2 and keeping track of the whole number part. I will demonstrate this using the equation tab
So 0.6640625 ten to binary =
[tex]0.1010_2[/tex]So to hexadecimal, 10 means A. So this becomes
[tex]\begin{gathered} 0.6640625\text{ }\times\text{ 16 = 10.625} \\ So\text{ we pick the whole number which is 10 } \\ \text{And 10 is A.} \\ \text{Next we multiply the decimal 0.625 by 16 = 10} \\ \text{And 10 is A} \\ \text{Therefore the answer is }0.6640625_2=0.AA_{16} \end{gathered}[/tex](b) 27.625 means 27 + 0.625
So we will convert both the whole number part and the decimal part to base 2 and base 16, then we combine to get the answer
[tex]\begin{gathered} 27\text{ to base 2} \\ \text{Divide by 2 and keep track of the remainder } \\ \text{read the remainder from bottom to the top} \\ 27_{10}=11011_2 \end{gathered}[/tex]Now the decimal part
[tex]\begin{gathered} \text{Just like I did above,} \\ m\text{ultiply the decimal 0.625 by 2 and note the whole number part} \\ 0.625\text{ }\times\text{ 2 = 1.250} \\ \\ 1.250\text{ }\times\text{ 2= 0.500} \\ \text{0.500 }\times\text{ 2 = 1.00} \\ \text{The whole number part from above is 101} \\ \text{This becomes 0.101}_2 \end{gathered}[/tex]Therefore
[tex]27.625_{10}\text{ to binary }=11011.101_2[/tex]To hexadecimal we will do the same, but 10 becomes A, 11 becomes B, 12 becomes C.
[tex]27_{10\text{ }}to\text{ decimal }=1B_{10}[/tex][tex]\begin{gathered} 0.625\text{ }\times\text{ 16 = 10.00 and 10 is A} \\ So\text{ }0.625_{10}\text{ to hexadecimal }=A_{16} \end{gathered}[/tex]Therefore
[tex]27.625_{10\text{ }}to\text{ hexadecimal }=1B.A_{16}[/tex]That is 1B.A to base 16
