CARLETON UNIVERSITY Final EXAMINATION April 13, 2009: 14:00

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1 RLETON UNIVERSITY Final EXMINTION pril 3, 29: 4: Name: Number: Signature: URTION: 3 HOURS No. of Students: 250 epartment Name & ourse Number: Electronics ELE 2607, and ourse Instructor(s) J. W. Rogers and J. Knight UTHORIZE MEMORN TURN OFF cell phones and personal communications equipment and LEVE THEM T THE FRONT. Notes, books, and non-communicating calculator are allowed. Students MUST count the number of pages in this examination question paper before beginning to write, and report any discrepancy immediately to a proctor. This question paper has 8 pages. This examination paper May Not be taken from the examination room. In addition to this question paper, students require: an examination booklet yes no x may request a Scantron sheet yes no x Please answer on the examination paper. If your answer does not fit, check you are not using a long hard methode. You may ask for a booklet if you need one. oolean For LL questions: If you use a map, indicate for which function it is. If you use algebra, indicate the rules used at the right side of each line. a) raw the simplest two-input gate, or one-input gate, or less, that are logically equivalent to the each of following: i) 0 ii) iii) b) onvert this circuit to real NOT, NN and NOR gates. For inversions, draw reasonable size bubbles, not black dots! h 0 c) Find the dual of k = ( + )( + ) + EF d) Simplify k = ( + )( + ) + EF (same expression as c) e) Loop the map shown, clearly and with no \ extra loops, and write the equation. Each d extra letter halves your mark. F = d d d d d d d d d d d d d page J. W. Rogers and J. Knight page of 8

2 arleton University Electronics ELE 2607, and Name 2 oolean and maps a),,, and are four input samples in a shift register, with the last one in being, and the first one. circuit is to give an output M=: - if at least 3 out of 4 of the input samples are zero, - and/or the first and last samples are zero. Write the equation for the circuit. 3% b) Given q = a + (c b + a + d) find q without using any overbars longer than one letter. four letter answer will be rewarded. 4% c) Find the simplest SUM-OF-PROUTS expression for the 5-variable function defined by the map below. lanks represent zeros. \ \ d d d d E=0 E= 4% d) Loop this dual output K-map to get expressions for F and G with a minimum gate count. im to get minimum logic, with gate count being the first priority. There is a spare set of maps. d d map of F map of G d d map of F map of G J. W. Rogers and J. Knight 2/9/09 page 2, of 8

3 arleton University Electronics ELE 2607, and Name 3 Machines with Storage a) What is the minimum number of flip flops one would need to design a synchronous machine to count from 0 to 24 in steps of 3. That is: 0, 3, 6, 9, 2, 5, 8, 2, 24, 0, 3, 6... b) For the -flip flop and waveforms shown, plot the output waveform. There is an asynchronous reset going in the LR input (Xilinx s notation). Logic LR asynchronous LR c) For the -flip flop and waveforms shown, plot the output waveform. There is a synchronous reset going in the R input (IEEE notation and Knight s, but not Xilinx s). Logic synchronous R R 5% d) Write out the state table for the output shown in the circuit below. state 0 + = lk next state + = = = = = = = = 0 0 Hint: Use the map The state table is in K-map order. + = + + 6% e) omplete the waveforms for and. Their initial values are both 0, as shown. sychronous I + I + =I J. W. Rogers and J. Knight 2/9/09 page 3, of 8

4 arleton University Electronics ELE 2607, and Name 7% 4 Waveforms from a circuit. LK Y E LR E E S X LR Y RST S Sketch the waveforms for, E, X, and Y. LK = E S X= Y RST t t 6% 5 Output waveforms from a state graph =0 Z= = Z= =0 Z= = Z=0 H=0 Z= G= Z=0 x= F=0 Z=0 E= Z=0 (i) oes this machine have a Meally output or a Moore output? Explain how you know. (ii) Hold x constant and plot the output waveforms. Start in state as shown Z for States for (iii)what is the relationship between the frequency of the clock and the frequency of the output? Z for x= States for x= (iv) What is the relationship between the frequency of the clock and the frequency of the output? (v) What might be the application of this circuit? J. W. Rogers and J. Knight 2/9/09 page 4, of 8

5 arleton University Electronics ELE 2607, and Name 4% 6 State Machines a) coin machine sells pictures of Steven Harper for (a dime). Inserting a dime closes a switch, and immediately, without waiting for the next clock edge, gives out a picture of Steven (see his pants coming out below). However, it will not give another picture until the coin rolls off the switch to open it, and another dime is put in. - raw the state graph. Our leader Warning: The dime may sit on the switch for many clock cycles. = means a dime is rolling over the switch. =0 when the switch is open and no dime is going over it. When output P= a picture is given out. Logic 5 khz LK The switch does not bounce ircuit P 5% b) nother coin machine sells pictures of Micheal Ignatieff for, but unfortunately it only takes nickles. Inserting a nickle closes a switch, but the machine does nothing until the first nickle rolls off the switch, opening it, and another nickle rolls on. Then it immediately gives out a picture of Micheal but will not give another one until the coin rolls off the switch to open it, and two more nickles are put in. - raw the state graph.. 5 Our opposition The switch does not bounce N= means a nickle is rolling over the switch. N=0 when the switch is open and no nickle is going over it. When output P= a picture is given out. Logic 5 khz LK N ircuit P 5% 7 ircuit from State Table State Using the state table below, draw a minimum gate-count circuit, including storage elements. State Table Next State + + X=0 X= Output z X=0 X= R = R= S= S= R= T= 0 T= S= T= H= S= S= 0 X 0 X 0 X 0 Map of Map of Map of J. W. Rogers and J. Knight 2/9/09 page 5, of 8

6 arleton University Electronics ELE 2607, and Name 5% 8 Programmable Logic a) Program the PL to implement the logic defined by the K-maps shown. Write the expression for each N over its input lead as indicated. write each N term here F G H Map of F Map of G (This is the only size of PL available to you.) Map of H 6% 5% b) Show how to implement the function g(,,,) defined by the Σ of Π map below using only MUXs and inverters. Minimization of hardware is expected. g = J. W. Rogers and J. Knight 2/9/09 page 6, of 8

7 arleton University Electronics ELE 2607, and Name 7% 9 State Reduction (i) Find the equivalent states in the table below. (ii) Make a new state table with the minimum number of states. State Next State X=0 X= G Output Z X=0 X= Revised State Table State Next State X=0 X= Output X=0 X= E J E H G J H J 0 J H 0 3% synchronous State ssignment x= x= x= x= x= x= The asynchronous state diagram on the left shows all of the transitions for a particular asynchronous machine. (i) Properly reroute any necessary transitions to eliminate races (ii) o a good state assignment for this machine on the. (iii) Put the state asignments inside the circles on the diagram. J. W. Rogers and J. Knight 2/9/09 page 7, of 8

8 arleton University Electronics ELE 2607, and Name 6% Hazards F = Modify the function F = E( ) + + E to minimize the number of gates, with the added condition you must mask all static- hazards. Write the minimal hazard free equation. ( 6 terms answer is best) E=0 E= 6% 2 synchronous ircuits i) Using the state graph below (all three graphs are the same), construct the asynchronous state-table. The state variables are P and, the inputs are a and b. ii) ircle the stable states. iii) Find a critical race either on the state graph or the state table. On the lower left graph, darken the copy of the transition that has the critical race. iv) Find any cycle(s) and darken its (their) arrows on the lower right state graph. arken arrows with races State variables P inputs ab arken arrows with cycles State table state p + q + ab= ab= ab= ab= P State table state p + q + ab= ab= ab= ab= P J. W. Rogers and J. Knight 2/9/09 page 8, of 8