In the IEEE $754$ floating point standard $($for double precision$),$ machine numbers are written in the following

form:

Where the cdots implies the intermediate digits are all zero.

To convert to a $($base ten$)$ decimal representation, we use the following formula:

$(-1{)}^s(1.f)2^{c-1023}$

Note that $c$ and $f$ must be converted to decimal numbers before applying this formula. $c$ is an integer number

and therefore the right most digit of its binary representation corresponds to $2^0,$ with the powers of $2$

increasing to the left. $f$ is the fractional part of the significand.

Find the decimal representation of the two following machine numbers.

a$)01000001000010010011000000$cdots$0$

b$)11000000110101010011000000$cdots$0$

number rtol $=1e-05,$ atol $=1e-06$