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: 68

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, \[D=68\]\[a=97\]\[d=100\] 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. \[\begin{align} & 68=\left( 1\times {{2}^{6}} \right)+\left( 0\times {{2}^{5}} \right)+\left( 0\times {{2}^{4}} \right)+\left( 0\times {{2}^{3}} \right)+\left( 1\times {{2}^{2}} \right)+\left( 0\times {{2}^{1}} \right)+\left( 0\times {{2}^{0}} \right) \\ & ={{1000100}_{\operatorname{two}}} \end{align}\] \[\begin{align} & 97=\left( 1\times {{2}^{6}} \right)+\left( 1\times {{2}^{5}} \right)+\left( 0\times {{2}^{4}} \right)+\left( 0\times {{2}^{3}} \right)+\left( 0\times {{2}^{2}} \right)+\left( 0\times {{2}^{1}} \right)+\left( 1\times {{2}^{0}} \right) \\ & ={{1100001}_{\operatorname{two}}} \end{align}\] \[\begin{align} & 100=\left( 1\times {{2}^{6}} \right)+\left( 1\times {{2}^{5}} \right)+\left( 0\times {{2}^{4}} \right)+\left( 0\times {{2}^{3}} \right)+\left( 1\times {{2}^{2}} \right)+\left( 0\times {{2}^{1}} \right)+\left( 0\times {{2}^{0}} \right) \\ & ={{1100100}_{\operatorname{two}}} \end{align}\] The binary sequence is \[\underline{1000100}\underline{1100001}\underline{1100100}\]. Binary representation for wordDad is\[100010011000011100100\].
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