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Q4. Floating-point numbers and arithmetic (a) For a B-based floating-point number system of p digits of precision, with exponent

Q4. Floating-point numbers and arithmetic
(a) For a B-based floating-point number system of p digits of precision, with exponent ranging from L to
U, find the total mumber of normalized floating-point number in terms of B,p, L.U.
(b) Let a be a nonzero real number and fl(a) be a k-digit rounding approximation to a in base 2.
Show that the relative error of round k-digits satisfy the bound
a-fla)
1* -f0
Ws
<2-*
Hint: Look at the two cases of rounding separately.
A lo lo ditela
the rounding
arrimotid
illal in hinn

Q4. Floating-point numbers and arithmetic (a) For a B-based floating-point number system of p digits of precision, with exponent ranging from L to U, find the total mumber of normalized floating-point number in terms of B,p, L.U. (b) Let a be a nonzero real number and fl(a) be a k-digit rounding approximation to a in base 2. Show that the relative error of round k-digits satisfy the bound a-fla) 1* -f0 Ws <2-* Hint: Look at the two cases of rounding separately. A lo lo ditela the rounding arrimotid illal in hinn

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