Department of Electrical and Computer Engineering University of Wisconsin - Madison. ECE/CS 352 Digital System Fundamentals.

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1 Last (family) name: First (given) name: Student I.D. #: Circle section: Lipasti Kim Department of Electrical and Computer Engineering University of isconsin - Madison ECE/CS 352 Digital System Fundamentals Quiz #1 Thursday, February 13, 2003, 7:15 8:30 PM Instructions: 1. Closed book examination. 2. No calculator, hand-held computer or portable computer allowed. 3. Five points penalty if fail to enter name, ID#, or instructor selection. 4. No one shall leave room during last 5 minutes of the examination. 5. Upon announcement of the end of the exam, stop writing on the exam paper immediately. Pass the exam to isles to be picked up by a TA. The instructor will announce when to leave the room. 6. Failure to follow instructions may result in forfeiture of your exam and will be handled according to US 14 Academic misconduct procedures. Problem Points Score Total 100 ECE/CS 352 Spring 2003 Quiz #1 February 13,

2 1. (20 points) number representations and conversion (a) (5 points) (63) 10 = ( ) 7 (b) (5 points) Determine the radix r for following case. (246)r = (132) 10 ECE/CS 352 Spring 2003 Quiz #1 February 13,

3 (c) (5 points) Find the Octal representation of the following Hexadecimal number: (8A3E.1) 16 = ( ) 8 (d) (5 points) Find the binary representation for the BCD number BCD ECE/CS 352 Spring 2003 Quiz #1 February 13,

4 2. (20 points) arithmetic operations, binary code (a) (10 points) Perform arithmetic operations in the following number representation. Indicate carries (for addition) and borrows (for subtraction) in addition to final answer. (5 points) Binary (5 points) Binary (b) (10 points) Perform the following BCD addition arithmetic operations in the space provided below. ou must show all your work to receive full credit ECE/CS 352 Spring 2003 Quiz #1 February 13,

5 3. (20 points) Boolean Algebra, Truth table, canonical forms (a) (10 points) Express the following Boolean function in minimized product of sum form. ou must show all your work to receive full credit. F(,, V, ) = V V (b) (10 points) Express the following Boolean function in a minimized sum of product form. ou must show all your work to receive full credit. F(A, B, C, D) =? M(1, 3, 6, 13, 14, 15). ECE/CS 352 Spring 2003 Quiz #1 February 13,

6 ECE/CS 352 Spring 2003 Quiz #1 February 13, (10 points) Boolean Algebra Prove the following identity, ),,, ( F, algebraically. = There is no need to explicitly list the use of commutative law as it is used frequently. ou may use all the Boolean identities listed at the end of this exam paper (page 10). ou should not need more than the spaces provided. Boolean Expression Boolean Identity used =

7 5. (15 points) Systematic Boolean simplification (a) (10 points) Express the function F(A, B, C, D) =? m(1, 5, 6, 8, 10, 11, 13, 15) using a minimized sum of product standard form. Find and list three different minimized sum of product forms for function F(A, B, C, D) with the minimum literal cost. ou must show all your work to receive full credit. (b) (5 points) Suppose the complements of inputs are not available and inputs are needed to be complemented for the use of each product term. Thus, use of the sum of product form with a minimum number of complemented literals is desired. hich sum of product term would you use among three possible sum of product forms you have found from part (a)? Using only a sentence or two briefly explain your reasoning. ECE/CS 352 Spring 2003 Quiz #1 February 13,

8 6. (15 points) Systematic Boolean simplification (a) (7 points) Consider the Boolean function below: F(a, b, c, d) =? M (1, 4, 5, 6, 9, 10). Find ALL the prime implicants of function F(a, b, c, d) using the tabular method. Answers without work will not receive any credit! ECE/CS 352 Spring 2003 Quiz #1 February 13,

9 (b) (8 points) A Boolean function g(w,x,y,z) consists of the following six prime implicants: w x z, w x y, w y z, w x z, w x y, y z Use a covering table, categorize these PIs into (i) Essential PI(s) (EPI), (ii) Less-than PI(s) (LTPI), (iii) Secondary Essential PI(s) (SEPI), or (iv) Redundant PI(s) (RPI). w x y z PI category ECE/CS 352 Spring 2003 Quiz #1 February 13,

10 Basic Identities of Boolean Algebra 1. 0 = 2. 1 = 3. 1 = = 0 5. = 6. = 7. =1 8. = 0 9. = 10. = 11. = Commutative Law 12. ( ) = ( ) 13. () = () Associative Law 14. ( ) = 15. = ( )( ) Distributive Law 16. = 17. = DeMorgan s Law Useful Boolean Identities 18. = 19. = 20. = 21. = 22. ( )( ) = 23. ( )( ) = ECE/CS 352 Spring 2003 Quiz #1 February 13,

Final Exam Solution Sunday, December 15, 10:05-12:05 PM

Final Exam Solution Sunday, December 15, 10:05-12:05 PM Last (family) name: First (given) name: Student I.D. #: Circle section: Kim Hu Department of Electrical and Computer Engineering University of Wisconsin - Madison ECE/CS 352 Digital System Fundamentals