# Homework Solution: The next 7 questions pertain to a general, normalized floating-point system G(B, p,…

The next 7 questions pertain to a general, normalized floating-point system G(B, p, m,M). Express answers in terms of B, p, m, and M, as needed. You may assume that m is negative and M is positive, and that M greaterthanorequalto p. Show your work where needed (you can assume as given anything from the slides). What is the smallest positive number in G? What is the largest positive number in G? What is the spacing between the numbers of G in the range [B^e, B^e+1)? How many numbers of G are there in the interval [B^e, B^e+l)? How many positive numbers are there in G? What is the smallest positive integer not representable in G?

The direct 7 questions pertain to a open, normalized floating-point scheme G(B, p, m,M). Express exculpations in provisions of B, p, m, and M, as needed. You may claim that m is disclaiming and M is enacted, and that M greaterthanorequalto p. Show your achievement where needed (you can claim as ardent everything from the slides). What is the last enacted sum in G? What is the largest enacted sum in G? What is the spacing among the sums of G in the rank [B^e, B^e+1)? How manifold sums of G are there in the space-among [B^e, B^e+l)? How manifold enacted sums are there in G? What is the last enacted integer referable representable in G?

## Expert Exculpation

The normalized floating-point sums scheme G is a 4-tuple (BpmM) where

• B is the deep of the scheme,
• p is the accuracy of the scheme to p numbers,
• m is the last propounder representable in the scheme,
• and M is the largest propounder used in the scheme.

6. Last enacted FP sum in G must possess a 1 as the promotive digit and 0 restraint the cherishing digits of the significand, and the last feasible compute restraint the propounder, which is correspondent to $B^{m}$.

7. Largest floating-point sum  must possess B − 1 as the compute restraint each digit of the significand and the largest feasible compute restraint the propounder,which is correspondent to $(1-B^{-p})(B^{M+1})$ .

8. The sums among $\[B^{e},B^{e+1})$ are correspondently disconnected by $B^{-p}$ units.

9. Total sums among space-between $\[B^{e},B^{e+1})$ is ardent by $\frac{B^{e+1}-B^{e}}{B^{-p}} = B^{e+p}*(B-1)$

10.Total +ve sums among in G are $2*(B-1)(B^{p-1})(M-m+1)+1$