#### Answer

a. 100.1
b. 10.11
c. 1.001
d. 0.0101
e. 101.101

#### Work Step by Step

a.
There are two parts in the given base ten representations. First
is integer part and the other is the fractional part.
$4\frac{1}{2}$ is equivalent to $4.5$
Step $1 :$ To convert the integer part of the base ten representations which is $(4)$ to its equivalent binary representations, we have to divide the number by $(2)$ until the quotient is zero, as shown in the table below.
\begin{equation}
\begin{array}{|c|c|c|}\hline \text { remainder } & {\text { divide by } 2} & {\text { number }} \\ \hline 0 & {2} & {4} \\ \hline 0 & {2} & {2} \\ \hline 1 & {2} & {1} \\ \hline & {2} & {0\ (stop)} \\ \hline\end{array}
\end{equation}
Therefore, the binary representation is the sequence of the remainder from bottom to top: $(4)_{10} = (100)_{2}$
Step $2 :$ To convert the fractional part of the base ten representations which is $( \frac{1}{2} = 0.5)$ to its equivalent binary representation, we have to multiply the fractional number by $(2)$ and keep track of the resulting integer and fractional part. Continue multiplying by $(2)$ until you get a resulting fractional part equal to zero. Then just write out the integer parts from the results of each multiplication from the top to bottom as shown below:
$0.5 * 2 = 1.0$
fractional part equal to zero. Then just write out the integer parts from the results of each multiplication from the top to bottom.
Therefore, $(0.5)_{10} = (0.1)_{2}$
Step $3 :$ concatenate integer part and fractional part
Therefore, $(4.5)_{10} = 100 + 0.1 = (100.1)_{2}$
----------
b.
$2\frac{3}{4}$ is equivalent to $2.75$
Step $1 :$ convert integer part (2) to binary
\begin{equation}
\begin{array}{|c|c|c|}\hline \text { remainder } & {\text { divide by } 2} & {\text { number }} \\ \hline 0 & {2} & {2} \\ \hline 1 & {2} & {1} \\ \hline & {2} & {0 (stop)} \\ \hline\end{array}
\end{equation}
Therefore, $(2)_{10} = (10)_{2}$
Step $2 :$ convert fractional part (0.75) to binary
$0.75 * 2 = 1.5 = 1 + 0.5$
$\ \ 0.5 * 2 = 1 \ \ \ = 1 + 0.0$
fractional part equal to zero. Then just write out the integer parts from the results of each multiplication from top to bottom.
Therefore, $(0.75)_{10} = (0.11)_{2}$
Step $3 :$ concatenate integer part and fractional part
Therefore, $(2.75)_{10} = 10 +0 .11 = (10.11)_{2}$