1. Round-off error results when a machine that stores numbers using finite bits performs floating point operations involving numbers of greatly different magnitude. Consider a machine that stores numbers as base 10 (B = 10) with 5 digits for the mantissa (aka the significand) and 1 digit for the exponent. (Note: technically there antissa there would also be an additional 1 bit reserved for the sign of the mantissa and one bit for the sign of the exponent.) (5pts) sulect result fro024, (a) Compute the roundoff error that would result from the following operation: 1.7421485.3 (3pts) (b) Compute the relative error that results from this operation. (1pt) (c) Compute the machine precision: € = B-(p-1), where p is the width of the mantissa. Note the similarity in magnitude between this quantity and the result from part b. (1pt)
1. Round-off error results when a machine that stores numbers using finite bits performs floating point operations involving numbers of greatly different magnitude. Consider a machine that stores numbers as base 10 (B = 10) with 5 digits for the mantissa (aka the significand) and 1 digit for the exponent. (Note: technically there antissa there would also be an additional 1 bit reserved for the sign of the mantissa and one bit for the sign of the exponent.) (5pts) sulect result fro024, (a) Compute the roundoff error that would result from the following operation: 1.7421485.3 (3pts) (b) Compute the relative error that results from this operation. (1pt) (c) Compute the machine precision: € = B-(p-1), where p is the width of the mantissa. Note the similarity in magnitude between this quantity and the result from part b. (1pt)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Round-off error results when a machine that stores numbers using finite bits performs
floating point operations involving numbers of greatly different magnitude. Consider
a machine that stores numbers as base 10 (B = 10) with 5 digits for the mantissa
(aka the significand) and 1 digit for the exponent. (Note: technically there antissa
there would
also
be an additional 1 bit reserved for the sign of the mantissa and one bit for the sign
of the exponent.) (5pts)
sulect result fro024,
(a) Compute the roundoff error that would result from the following operation:
1.7421485.3 (3pts)
(b) Compute the relative error that results from this operation. (1pt)
(c) Compute the machine precision: € = B-(p-1), where p is the width of the
mantissa. Note the similarity in magnitude between this quantity and the result
from part b. (1pt)
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