MASSACHVSETTS INSTITVTE OF TECHNOLOGY 6.004 ...

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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
Problem Set #2 page 7 of 8Problem 6: Latches and Flip-flops [No Collaboration]Given the following sequences A and B, draw the timing diagrams for the outputs Q1, Q2,and Q3. All the signals are positive logic, and reset overrides set on the RS Latch. Assumesetup and hold times are met in all cases and that the propagation delay is negligible. Also,assume a low signal as the initial value for Q1, Q2, and Q3.ABTransparent latchD flip-flopRS LatchABDGQQ1 A D QBQ2ABRSQQ36.004 Spring 1997 2/11/97
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