Q4. Floating-point numbers and arithmeti

Question

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

Kunduz · Accepted Answer

Given system of p-dage formula is a su B - based floating point number digits of precision with exponent ranging for 2 to o , have to find the total no. of normalized floating point number terms of ß,plu. - Here Floating point number system characterized by entergers ß Bax on) dadine - P = precision [1,0] - Exponent range dez dp-1/B ald Four 11 bu Lu . E 3 YO - Number srp verende a P-) x = + *(dat die + Bº BP2 les + da B² +da de, do di B + } s ß² where -10 Floating - pornt System Deimalized 16 leading doet do always nonna zor unless number apresented & - Floating point number system finite & discrete & . No. Normalized froating floating - point numbers: ( 2 (B-1) "(0-2+1)+1 p--) Smallest tre normalized numbes : underflow level => largest floating point nautes: over flow lovel . floting point number equaly spaced only be powers of B. & for not heal numbers only for machine numbers B6+%C-PP) -

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