Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 4 - Number Representation and Calculation - 4.2 Number Bases in Positional Systems - Exercise Set 4.2 - Page 226: 67

Answer

The capital letters A through Z are assigned 65 through 90. The lower-case letters a through z are assigned 97 through 122. Accordingly, \[M=77\],\[o=111\]and \[m=109\] Convert each base ten number to binary by repeated division by 2 with the remainder obtained or mentally convert by forming groups of place-value. \[\begin{align} & 77=\left( 1\times {{2}^{6}} \right)+\left( 0\times {{2}^{5}} \right)+\left( 0\times {{2}^{4}} \right)+\left( 1\times {{2}^{3}} \right)+\left( 1\times {{2}^{2}} \right)+\left( 0\times {{2}^{1}} \right)+\left( 1\times {{2}^{0}} \right) \\ & ={{1001101}_{\operatorname{two}}} \end{align}\] \[\begin{align} & 111=\left( 1\times {{2}^{6}} \right)+\left( 1\times {{2}^{5}} \right)+\left( 0\times {{2}^{4}} \right)+\left( 1\times {{2}^{3}} \right)+\left( 1\times {{2}^{2}} \right)+\left( 1\times {{2}^{1}} \right)+\left( 1\times {{2}^{0}} \right) \\ & ={{1101111}_{\operatorname{two}}} \end{align}\] \[\begin{align} & 109=\left( 1\times {{2}^{6}} \right)+\left( 1\times {{2}^{5}} \right)+\left( 0\times {{2}^{4}} \right)+\left( 1\times {{2}^{3}} \right)+\left( 1\times {{2}^{2}} \right)+\left( 0\times {{2}^{1}} \right)+\left( 1\times {{2}^{0}} \right) \\ & ={{1101101}_{\operatorname{two}}} \end{align}\] The binary sequence is \[\underline{1001101}\underline{1101111}\underline{1101101}\]. Binary representation for word Mom is \[100110111011111101101\]
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