a$)($True$/$False$)$ If n $=2$k

$,$ then dlg ne $=$ k$.$

$($b$)($True$/$False$)$ If n $=2$k

$,$ then blg nc $=$ k$.$

$($c$)($True$/$False$)$ Any integer n can be written as

$2$k$1<=$ n $<2$k $($sandwich any n$?)$

$($d$)$ How many bits does it take to write a number

n such that $2$k$1<=$ n $<2$k$?$

$($e$)$ In exercise $1\mathrm{.}3($a$)$ you concluded that

dlg $35$e $=6,$ and in exercise $1\mathrm{.}3($d$)$ you con$-$

cluded that the number $35$ is six bits long: $35$

in binary is $100011.$

So$,$ is it true that dlg ne is the length of n writ$-$

ten in binary? Explain your answer clearly.

$($f$)$ How many bits do you need to express n $>0$

in binary? Give an exact expression.