This problem considers how to determine the largest value of the mantissa. (a) What values of the j ’s in (1.7) produce the largest value of ? (b) Assuming    1, show that...

This problem considers how to determine the largest value of the mantissa.

(a) What values of the


_j
’s in (1.7) produce the largest value of
?

(b) Assuming
 1, show that

(c) Use the result from part (b) to show that the value of
 from part (a) can be written as
 = 2 −
. From this show that the largest value of the mantissa is
 =1+
, where
 = 2
<sup>N

−1</sup>
− 1.

(d) Use part (c) to explain why the float just to the left of
 = 2 is 2 −
. Also, explain why the float just to the right of
 = 2 is 2(1 +
).