Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 16 - Review: 4

Answer

$22\frac{3}{4}$

Work Step by Step

Just as each digit of a standard Base 10 number has a place value that is a power of 10, each digit of a binary, or Base 2, number has a place value that is a power of 2. Reading right to left from the decimal point, the exponent starts at 0 and increases by 1. Reading left to right from the decimal point, the exponent starts at -1 and decreases by 1. $\underset\uparrow1\ \ \ \ \underset\uparrow0\ \ \ \ \underset\uparrow1\ \ \ \ \underset\uparrow1\ \ \ \ \underset\uparrow0\ \ .\ \ \underset\uparrow1\ \ \ \ \underset\uparrow1\ \ \ \ $ $2^4\ \ 2^3\ \ 2^2\ \ 2^1\ \ 2^0\ \ \ 2^{-1}\ \ 2^{-2}\longrightarrow$ place value Multiply each non-zero digit by it's place value (using Base 10 computations) and find the sum of each. $(1\times2^4) +(1\times2^2)+(1\times2^1)+(1\times2^{-1})+(1\times2^{-2})=16+4+2+\frac{1}{2}+\frac{1}{4}=16+4+2+\frac{2}{4}+\frac{1}{4}=22\frac{3}{4}$
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