$1$a$.$ In $4\mathrm{.}2$ you learned how to convert binary to octal and to hexadecimal directly. Based

on what you learned, describe how you can covert binary to base $4,$ and from base $4$

to hexadecimal. Verify that you have a correct algorithm by converting the following

number

$(10011001111001)\_(2)$

to base $4$ number, and then covert the number in base $4$ to hexadecimal. Covert the

above number to hexadecimal using the procedure described in the textbook and then

compare the two answers you have.

$1$b$.$ The set $\{11$ a$+7$b$$a$,$b inZ$\}$ is equal to a familiar set. By examining which elements

are possible, determine the familiar set. $($Hint: if examining alone doesn't help, the

concept of relatively prime, Euclidean algorithm, and Bezout's theorem may be useful

see $4\mathrm{.}3).$