AMATH242 Study Guide - Midterm Guide: Machine Epsilon, Fast Fourier Transform, Linear Interpolation

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Am 242 / cs 371 - midterm examination. Signature: ensure that your uwaterloo email, name and id number appear correctly at the top of this page. Sign above in ink: there are questions on both sides of the pages, answer the questions in the spaces provided. If you require additional space to answer a question, please use the last page and refer to that page in your solutions: do not write on the qr code that appears on each page. 2: (4 marks) consider the same normalized oating-point number system used in question 1: F l(10, 4, 2) corresponding to base 10, four digits for the normalized mantissa, and two digits for the exponent, that uses rounding when storing real numbers in its exponent range. Nonzero numbers have the form: 0. d1d2d3d4 10 e1e2, where d1 6= 0. Verify that the absolute value of the relative error for your method is smaller.