$($theoretical$,3$ points$)$ We use again the binary floating point number system $F$ from Q$2$

$($with $1$ bit for sign, $7$ bits for mantissa and $5$ bits for exponent$).$ And consider now another

binary floating point number system widetilde$(F)$ with $1$ bit for sign, $11$ bits for mantissa and $5$ bits for

exponent. How many normalized numbers in widetilde$(F)$ can you find in $(z_1,z_2),$ with $z_1$ and $z_2$ being

two consecutive normalized numbers in $F?$ You will only earn $1$ point if you correctly list

out two example adjacent numbers in $F$ and then count the widetilde$(F)$ numbers in between.