## Numerical Methods for Engineers and Scientists

Published by Wiley

# Chapter 1 - Section 1.5 - Problems - Page 18: 1.3

#### Answer

$\approx$ 11377.33984375

#### Work Step by Step

1 0 1 1 0 0 0 1 1 1 0 0 0 1. 0 1 0 1 0 1 1 1 (binary number) 13-12-11-10-9-8-7-6-5-4-3-2-1-0-(-1)-(-2)-(-3)-(-4)-(-5)-(-6)-(-7)-(-8) (Position/index) A quicker way to change binary numbers to a decimal number is to look only at which position there is a 1, for zero times anything is always zero. For the first part: $2^{13}+2^{11} + 2^{10} + 2^{6} + 2 ^{5} + 2^{4} + 2^{0} = 11377$ Second part: $2^{-2} + 2^{-4} + 2^{-6} + 2^{-7} + 2^{-8} \approx 0.33984375$ Add the two numbers together: 11377+ 0.33984375 = 11377.33984375

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