Question $3$: Simplify the following Boolean function using the Karnaugh Map. Sketch the circuit diagram

for each minimized implementation of the function.

$($a$)F(A,B,C)=m(1,3,4)$

$($b$)G(w,x,y,z)=m(0,7,8,10)$ with don't care terms being $d(1,4,5,13)$

Question $4$: Consider a Boolean function $f(a,b,c,d)(4$ binary inputs: $a,b,c,d,$ and $1$ output$)$ that outputs

the value of

Don't care if inputs are $0000$ or $1111$

$0$ if the number of $1\text{'}$s in $a,b,c$ and $d$ is an even number, except $0000$ and $1111$

$1$ if the number of $1\text{'}$s in $a,b,c$ and $d$ is an odd number

$($a$)$ Write a truth table for function $f.$

$($b$)$ Construct $K-$map for function $f,$ and write the minimal expression for function $f$ in the sum$-$of$-$product

$($SOP$)$ and product$-$of$-$sum $($POS$)$ forms. Clearly show all the groupings.