IEEE $754$ single precision specifies that $23$ binary bits are used for the value f

in the significand$1+$f

in $(1\mathrm{.}1\mathrm{.}2).$ Because they need less storage space and can be operated on more quickly than double$-$precision values, single$-$precision values can be useful in low$-$precision applications. $($They are supported as type Float$32$ in Julia.$)$

$($a$)$ In base$-10$ terms, what is the first single$-$precision number greater than

$1$

in this system?

$($b$)$ What is the smallest positive integer that is not a single$-$precision number? $($See the hint to Exercise $1.)$