$[6]$ Simplify the following Boolean equations using Boolean algebra laws. Check for correctness using a truth table.

$($a$)$ Y$=$A'BC$+$A'BC'

$($b$)$ Y$=$ A'B'C'$+$AB$\text{'}$

$[5]$ Sketch the circuit implementing the following Boolean equation.

$Y=B\text{'}+(B\text{'}C\text{'}+A)$

$[7]$ Convert the following numbers to the base given in the question mark.

$($a$){0001111}_2={?}_{10}$

$($b$){127}_{10}={?}_{16}$

$($c$)$ OxFA $={?}_{10}$

$($d$){100011110101000010101011}_2=16$

$($e$){10111111}_2={?}_{10}$

$($f$)023={?}_{10}$

$($g$){135}_{10}={?}_2$

$[4]$ Perform the following number conversions:

$($a$)$ OXABCOF$1$ to binary

$($b$)$ Binary $110000011001111$ to hexadecimal

$[4]$ Convert between decimal and hexadecimal:

$($a$)147$ to hexadecimal

$($b$)$ OXAE to decimal

$[9]$ Perform the following operations on $x=0A5$ and $y=02C($answer in hex$)$:

$($a$)x$&$y$

$($b$)x$&&$y$

$($c$)((x^{{?}^{?}}y)|)$