{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIDF06_ANS_revised

# MIDF06_ANS_revised - ECSE-323 Department of Electrical and...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Question 1 :Boolean Logic Theory (10 points) (5 points) a) Produce the Shannon expansion of F with respect to variables A and C. F(A,B,C,D) = A B + f8e5 C f8e5 B + D f8e5 A + f8e5 B f8e5 D + A C. (5 points) b) Using DUALITY convert the following sum-of-products expression into its product-of-sums equivalent . F(A,B,C,D) = A f8e5 D f8e5 C + B A D + f8e5 A C D + f8e5 B C D. ___________________________________________________________________________ ANSWER: a) F(A,B,C,D) = f8e5 A f8e5 C [F(0,B,0,D)] + f8e5 A C [F(0,B,1,D)] + A f8e5 C [F(1,B,0,D)] + A C [F(1,B,1,D)]. F(A,B,C,D) = f8e5 A f8e5 C [ f8e5 B + D + f8e5 B f8e5 D ] + f8e5 A C [ D + f8e5 B f8e5 D ]+ A f8e5 C [B + f8e5 B + f8e5 B f8e5 D ] + A C [1]. F(A,B,C,D) = f8e5 A f8e5 C [ f8e5 B + D] + f8e5 A C [ f8e5 B + D ]+ A f8e5 C [1 ] + A C [1]. b) F Dual = (A + f8e5 D + f8e5 C)( B + A + D)( f8e5 A + C + D)( f8e5 B + C + D). F Dual = (AB + A + AD + f8e5 DB + f8e5 DA + f8e5 CB + f8e5 CA+ f8e5 CD)( f8e5 A f8e5 B + f8e5 AC+ f8e5 AD+ C f8e5 B+ C + CD + D f8e5 B + DC + D). Simplifying terms within each parenthesis (applying xy + x = x), we obtain F Dual = (A + f8e5 DB + f8e5 CB + f8e5 CD)( f8e5 A f8e5 B + C + D). Expanding F Dual = AC + AD + f8e5 DBC + f8e5 CBD + f8e5 C D f8e5 A f8e5 B + f8e5 C D = AC + AD + f8e5 DBC + f8e5 C D Taking the dual of F Dual to obtain F in POS form, the result is F = (F Dual ) Dual = (A + C)(A+D)( f8e5 D + B + C)( f8e5 C + D).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.
• Winter '07
• redacka
• Logic gate, XOR gate, Combinational circuit design, Name_______________________________________________________ Question

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern