Numerical analysis, Need Help with part (c) of this question Given a floating po

Question

Numerical analysis, Need Help with part (c) of this question

Given a floating point system (beta, t, L, U) = (10, 4, -3, 3), where beta is the base, t is the number of significant digits, L and U are the lower and upper bound of the exponent respectively. (a). What are the floating point representation of the real numbers x = 4.312809 and y = 0.4312809 if the rounding strategy is used? (note that the first digit d_0 notequalto 0) (b). What is the rounding unit eta of this floating point system? (c). Which of the following four numbers will cause the problem of underflow or overflow if it is represented by this floating point system? A) 0.0051: (B) 0.00000001: (C) 12000: (D) -12000.

Explanation / Answer

(c). Overflow = B^(U+1) [1-B^(-t)]

=(10^4) (1-(10^-4))

= 9999

Underflow = B^L

=10^(-3)

=0.001

Thus (C) 12000 is Overflow

And (D) -12000 is Underflow

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