Answer the following questions:

$8M$:$3+4+1$

a$)x=0111110$ and $Y=1100001$ are two $7$bit binary number represented in $2\text{'}$s complement format. How $x-Y$ is computed using $2\text{'}$s complement $8-$bit format?

b$)$ Simplify the following using $K-$map and realize the simplified expression NAND gates only.

$F=A{B}^{\text{'}}{C}^{\text{'}}+A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}+A^{\text{'}}{B}^{\text{'}}+A^{\text{'}}{C}^{\text{'}}+A{C}^{\text{'}}$

C$)$ State one main difference between von$-$Neumann Architecture and Harvard Architecture.