MASSACHVSETTS INSTITVTE OF TECHNOLOGY 6.004 ...

page 6 of 8 Problem Set #2Problem 3: Gates, can they be hazardous to your health? [To be done without collaboration]Shown below is a CMOS implementation of a logic gate. In this problem we willdetermine the whether it has input hazards.AOUTBA. Hazards can potentially occur when there is a transition from one input state toanother. List all state transitions with potential hazards. Remember that the only hazardswe care about in 6.004 are those that result from 1 input bit changing.B. For the transition 00 -> 01 argue why it either does (or does not) have a hazard.C. Does this circuit have any hazards?Problem 4: Karnaugh Maps [No Collaboration]f = A C + A B C + A C DA. Draw the Karnaugh map of the Boolean function f. Circle the implicants that correspondto each product term from the Boolean expression above.B. Label the hazards that would result if f were implemented using the implicants circledin Part A.C. Write out the minimal Sum of Products form for f which is hazard free (i.e. the resultingexpression should have the fewest possible product terms and no hazards).Problem 5: The Muller C Element [No Collaboration]A. Do Problem 4.2 from the text.Note: The Muller C element is used in asynchronous computing2/11/97 6.004 Spring 1996