$[2$ points$]$ Find the minimum number of bits $($n$)$ needed to represent $($encode in

binary$)$ the different number of objects $($N$)($items$)$ listed below:

a$.1027$

b$.31,415,926,535$

$2.[20$ points$]$ a$)$ Carry out the conversions required to complete the columns.

BINARY OCTAL DECIMAL HEXADECIMAL

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_183\mathrm{.}75\_\_\_\_\_\_\_\_\_\_\_$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ BC$\mathrm{.}4$

$1110111\mathrm{.}101\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$)$ Find the NUMBER first and then find the other representations.

Number $1$s Complement $2$s Complement MAGNITUDE SIGN

$110010\mathrm{.}00101101\mathrm{.}11001101\mathrm{.}11110010\mathrm{.}001$ negative

$10110111\mathrm{.}01$

$111110110\mathrm{.}01$

$01111111\mathrm{.}01$

$3.[20$ points$]1)$ Convert to base $7$ the following number BAD.CE$16($do all the

arithmetic in decimal$).2)$ Also find the binary, octal and decimal representation of

the hexadecimal number.