## Computer Science: An Overview: Global Edition (12th Edition)

Published by Pearson Higher Education

# Chapter 1 - Data Storage - Section 1.5 - The Binary System - Questions & Exercises - Page 57: 2

#### Answer

solution is shown in the table below: \begin{equation} \begin{array}{|c|c|c|}\hline & {\text { Base } 10} & {\text { Equivalent Binary form }} \\ \hline \mathrm{a} & {32} & {100000} \\ \hline \mathrm{b} & {64} & {1000000} \\ \hline \mathrm{c} & {96} & {1100000} \\ \hline \mathrm{d} & {15} & {1111} \\ \hline \mathrm{e} & {27} & {11011} \\ \hline\end{array} \end{equation}

#### Work Step by Step

a. Step $1 :$ To convert the base ten representations to its equivalent binary representations, 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 number by } 2} & {\text { number }} \\ \hline 0 & {2} & {32} \\ \hline 0 & {2} & {16} \\ \hline 0 & {2} & {8} \\ \hline 0 & {2} & {8} \\ \hline 0 & {2} & {2} \\ \hline 0 & {2} & {2} \\ \hline 1 & {2} & {1} \\ \hline & {2} & {0} \\ \hline\end{array} \end{equation} Step $2 :$ Therefore, the binary representation is the sequence of the remainder from bottom to top Therefore, $(32)_{10}=(1000000)_{2}$ ---- to solve [ b, c, d, e ] do the previous steps : b. the solution is: 1000000 c. the solution is: 1100000 d. the solution is: 1111 e. the solution is: 11011

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