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: 61

Answer

The binary code for $F$ is: $1000110$

Work Step by Step

The essay states that the uppercase letter $F$ is assigned the number $70$. To find the binary representation for this, use division. The place values in base two are $..., 2^7, 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 1$ The place values that are less than or equal to $70$ are $2^6, 2^5, 2^4, 2^3, 2^2, 2^1$ and $1$. Divide $70$ by $2^6$ or $64$: $70 \div 64 = 1$ remainder $6$ Divide $6$ by $2^5$ or $32$ $6 \div 32 = 0$ remainder $6$ Divide $6$ by $2^4$ or $16$: $6 \div 16 = 0$ remainder $6$ Divide $6$ by $2^3$ or $8$: $6 \div 8 = 0$ remainder $6$ Divide $6$ by $2^2$: $6 \div 4=1$ remainder $2$ Divide $2$ by $2^1$ or $2$: $2 \div 2 = 1$ remainder $0$ Divide $0$ by $1$: $0 \div 1 = 0$ Thus, $70 = 1000110$
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