Question $1$: $[50$ pts$.]$

For the following boolean function:

$F(x,y,z,t)=(x^{\text{'}}y+x{y}^{\text{'}})t+y^{\text{'}}(x^{\text{'}}z+t^{\text{'}}x)+z{x}^{\text{'}}$

a$)$ Without any simplification, implement the function using NOR gates only.

b$)$ Write the function canonically as a sum of minterms, i$.$e$.,$ and then write it as a product of maxterms, i$.$e$.).$

c$)$ Using Karnaugh$-$map, simplify the function as sum of products and implement it using NAND gates.

d$)$ Implement the function using $41$ multiplexer and external gates.

e$)$ Write a verilog description for the simplified function in part $($c$),$ i$.$e$.$ for sum of products.