Answer the following and show your work:

a$)$ Using the consensus theorem and the absorption theorem, find all prime

implicants $($PIs$)$ of the function

$F(A,B,C)=\frac{A}{b}ar(B)+\frac{B}{b}ar(C)\frac{+}{b}ar(A)C$

$[$continued on next page$]$

Homework $4$

b$)$ Show that there are no essential prime implicants $($EPIs$).$ Use the procedure

described in lecture $($i$.$e$.,$ if a PI is removed and can be regenerated via

consensus, then the PI is a non$-$essential PI; otherwise the PI is an EPI; do

this for each PI$).$

c$)$ Following the procedure described in lecture, find the MSOP form of $F,$

d$)$ Illustrate all PIs on a Karnaugh map, Label each PI and briefly discuss

which PIs you incorporated into your MSOP and which PIs you did not

incorporate into your MSOP. Provide a brief and technically concise answer

to the following question: is your MSOP unique, or could you have chosen

an alternative MSOP? Explain.