Why is binary arithmetic employed by digital computers?

$(2$ Marks$)$

Draw a truth table to represent the intermediate values and output of the circuit below. What is the Boolean expression being solved?

$(14$ Marks$)$

Simplify the following Boolean expression using identities and state the indent used per step:

$F(x,y)=(xy{)}^{\text{'}}(x^{\text{'}}+y)(y^{\text{'}}+y)$

$(12$ Marks$)$

$16.$ The stored$-$program machine architecture satisfies at least three things: hardware systems, instruction and path. Discuss.

$(10$ Marks$)$