Digital Electronics: Hamming Distance, ALU Design, Sequential Logic, Error Detection, Exams of Computer Architecture and Organization

Download Digital Electronics: Hamming Distance, ALU Design, Sequential Logic, Error Detection and more Exams Computer Architecture and Organization in PDF only on Docsity! 1. (1pts) What is the Hamming distance between these two bit patterns: 101101 and 101010? 2. (2pts) Write the equation for the carry out of the 4th adder cell in an ALU using carry- lookahead, in terms of P’s and G’s. 3. (3pts) Using a 4-1 mux, implement the following function: (X AND Y) OR (X AND !Z) OR (!Y AND !Z) 4. (4pts) What is the difference between the Mealy and Moore models of sequential design? What is the advantage to the Moore approach? 5. (2pts) What is the difference between a Flip-Flop and a latch? 6. (3pts) In the ALU you designed in the homework, how did you differentiate between an operation being an "add" and an operation being a "subtract"? In other words, what bit/bits were set/cleared in order to indicate that the values were to be added instead of subtracted? Why did this work so well? 7. (10 pts) Assuming rising edge-triggered flipflops, what is the maximum clock frequency possible for the following circuit? (In other words, what is the maximum clock frequency that will still guarantee correct behavior?) Use the following delay values, and assume all input signals become valid at time 0. (Tprop is the propagation time for the flipflop, the time it takes from the rising edge of the clock until the output of the FF is valid.) AND: 3ns NAND: 4ns NOT: 2ns MUX: 5ns Tprop (DFF): 7ns Tsetup (DFF): 2ns Thold (DFF): 3ns Tprop (TFF): 8ns Tsetup (TFF): 3ns Thold (TFF): 2ns Tprop (JKFF): 9ns Tsetup (JKFF): 4ns Thold (JKFF): 2ns 1 0 1 0 1 0 1 0 Q DFF Q Q ClockSEL Q TFF Y JKFF DFF 11. (16) Given the following table, draw the Karnaugh maps for Y1’, Y2’, and Y3’ and Z in terms of X, Y1, Y2 and Y3, and then write minimum boolean equations for each. Present Next State Output State X=0 X=1 X=0 X=1 (Y1 Y2 Y3) (Y1’ Y2’ Y3’) (Y1’ Y2’ Y3’) 000 111 010 0 0 010 110 010 0 1 100 010 010 0 0 101 000 111 1 0 110 000 000 0 0 111 000 101 1 0 X Y1 Y3 X Y1 Y2 X Y1 Y2 Y3 Y2 Y3 X Y1 Y3 X Y1 Y2 X Y1 Y2 Y3 Y2 Y3 12. (15 pts) Given the following Karnaugh maps, implement the sequential machine using an SR FF for Y1, a JK FF for Y2, and a T FF for Y3. You do not need to draw the gates, but you do need to write down the minimized input equations for each of the inputs of each of the Flip Flops in the circuit. X Y3 Y1 Y2 X Y3 Y1 Y2 X Y3 Y1 Y2 Y1’ Y2’ Y3’ 1 1 d 1 1 d d d1 1 1 1 1 1 d 1 1 1 d 1 1 1 1 1 1 d 1 X Y1 Y3 X Y1 Y2 X Y1 Y2 Y3 Y2 Y3 X Y1 Y3 X Y1 Y2 X Y1 Y2 Y3 Y2 Y3 13. (20 pts) The President of Freedonia (Rufus T. Firefly) suspects his Prime Minister has been using the presidential restroom without permission. The President is incredibly cheap, but not without heart - therefore, has decided to make some modifications and turn it into a pay toilet with a twist: you don’t hav e to pay to get in, but you have to pay to get access to the toilet paper. (Gives new meaning to the phrase "pay as you go", doesn’t it? :-) You have been hired to make the necessary modifications. The President wants the toilet paper dis- penser to accept two coins, the 5 Quatloo piece (the "nickeloo") and the 10 Quatloo piece (the "dimeloo"). Access to the toilet paper costs 25 Quatloos, and the dispenser must give change. Let X1 be the ten Quatloo coin and X2 the five Quatloo coin, and assume both coins cannot be inserted simultaneously (no matter how much of a hurry the user is in.) Therefore, 10 = a dimeloo inserted, 01 = a nickeloo. Draw the State Transistion Diagram (the circles and the arcs) for this finite state machine. Let S0=no money input (the Start state). Once you have a state transition diagram, mini- mize the number of states necessary and then assign bit patterns to each state and write down the corresponding state transition table. Assume you are using a Mealy model. Label the transitions on the diagram using the format we used in class (inputs over outputs).