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7. (Graduate Problem) Let F denote the (normalized) double-precision numbers, excluding too,

NaN and the signed zeros, i.e. F only consists of 0 and those numbers that can be expressed

52

10

where E = 2¹0-k

as (-1) 1+

1² (1 + 2√2-1) ₂25

d2

k=1

2E-1023

k=0

(a) How many numbers are in F.

(b) Assuming that -1022 ≤e < 1023, how many numbers are there in [2€, 2e+1) nF where n

is the "intersect" sign represents the set of elements that are in both sets.

Fig: 1