Numerical Analysis Question:

1. For the normalized floating point system (2,5,-5, 7) A. What is the rounding unit? B. Estimate the absolute error f)and relative error errorby chopping and rounding (use C. Use the result in Part B to estimate the errors of the floating point representation of 105 the results in the Theorem) Theorem: Floating Point Representation Error. Let x-f (x) = g x e, where x 0 and g is the normalized, signed mantissa Then the absolute error committed in using the floating point representation of x is bounded by B1-.pe for chopping, e for rounding, flx) 1.ge whereas the relative error satisfies for chopping, B- for rounding. 1. For the normalized floating point system (2,5,-5, 7) A. What is the rounding unit? B. Estimate the absolute error f)and relative error errorby chopping and rounding (use C. Use the result in Part B to estimate the errors of the floating point representation of 105 the results in the Theorem) Theorem: Floating Point Representation Error. Let x-f (x) = g x e, where x 0 and g is the normalized, signed mantissa Then the absolute error committed in using the floating point representation of x is bounded by B1-.pe for chopping, e for rounding, flx) 1.ge whereas the relative error satisfies for chopping, B- for rounding