Using the $8-$bit $2$s complement number system, perform the following operations

If X$=(87)10$ and Y$=(53)10.$

Identify any overflow and explain. Show your work for full credit

a$.$ X $+$ Y

b$.$ Y $$ X

c$.-$X $$ Y

d$.$Y $+$ X

$2.20$ points, each $10$ points

For the circuit below of three inputs x$,$ y and z:

a$.$ Give truth table of the circuit

b$.$ Give expression for the output F$2$

$3.$ Using Boolean Algebra to simplify the following expressions to the simplest form

possible. $10$ points each

a$.$ xyz$+$ xy$$z$+$ x$$y

b$.$ AB$+$ ABC $+$ AC$$D