Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 4 - Section 4.2 - Integer Representations and Algorithms - Exercises - Page 255: 3

Answer

a.) 31₁₀ b.) 513₁₀ c.) 958₁₀ d.) 26896₁₀

Work Step by Step

We will be using Doubles Up Method 1st: Count off the digital places of the binary.(The total places will be represented by ᶦ•ˢ) 2nd: Use the formula 2ᶦ•ˢ⁻¹ 3rd: After computing 2ᶦ•ˢ⁻¹, multiply the answer by 2.( Multiplying 2 is always constant.) 4th: Subtract the answer by 1.(Subtracting 1 is always constant) 5th: Mark down all the 0's in the given and write down their respective places. (Always start from 0 and count from right to left.) 6th: Insert those places as exponent of 2. Compute the sum afterwards. (e.g. 2¹+2²+2³+2⁴) 7th: Subtract your answer from 4th and 6th.
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