Sequential Design_ Even_Odd Circuit

Sequential Design_ Even_Odd Circuit - Mallard ECE 290:...

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Unformatted text preview: Mallard ECE 290: Computer Engineering I - Spring 2007 - Graded WebQuiz : Sequential... Page 1 of 5 Graded Graded WebQuiz : Sequential Design: Even/Odd Circuit You have submitted this WebQuiz 1 time (including this time). You may submit this WebQuiz a total of 10 times and receive full credit. In this WebQuiz you are allowed to "go back" but at most 10 submissions are allowed. Word Description Design a 2-state sequential network with a single input x and a single output z, which outputs: 1 if the number of 0's read thus far is even, and 0 if the number of 0's read thus far is odd State Diagram You may wish to first draw a state diagram. State Table Complete the next-state table. There are 2 states, A and B. Before filling in the table, be sure you have clearly in mind the meaning of each state. What is it we need to "remember"? The only past history important to us is whether the total number of 0's read thus far is even or odd. Hence, we will have 2 states: A: the number of 0's read thus far is even. B: the number of 0's read thus far is odd. Which state is the start state? A Current State Input (x) Next State Output (z) A 0 B 0 A 1 A 1 B 0 A 1 B 1 B 0 State State Assignment There are 2 states, and so a single flip-flop is needed. Accordingly, there will be a single state variable Q. We arbitrarily choose the following state assignment: A = 0, B = 1 https://mallard.cites.uiuc.edu/ECE290/webgrade.cgi?SessionID=mding3_1070311_13325... 3/11/2007 Mallard ECE 290: Computer Engineering I - Spring 2007 - Graded WebQuiz : Sequential... Page 2 of 5 Complete the state table below, using the above state assignment. Current Current State Input Next State Output Q x Q+ z 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 Your points: 100.00 Determine Determine the Output Functions Q'x+Qx' z(Q,x) = Q'x+Qx' Enter a minimal SOP Boolean expression FlipFlipDecide Type(s) of Flip-Flops to Use and Determine Flip-Flop Excitation Functions To implement this network we need a single flip-flop: D, T, JK, or SR. In this exercise we will get lots of practice and implement the network 4 separate times. Determine equations for the flip-flop inputs. When completing the state tables, be sure to use don't cares wherever possible. FlipOption 1: A D Flip-Flop Implementation Give a D flip-flop implementation, by providing the excitation input values in the table and then giving a minimal SOP expression for D. Current Current State Input FF Excitation Q x D 0 0 1 0 1 0 1 0 0 1 1 1 D(Q,x) Q'x'+Qx D(Q,x) = Q'x'+Qx Enter a minimal SOP Boolean expression Your points: 100.00 FlipOption 2: A JK Flip-Flop Implementation Give a JK flip-flop implementation, by providing the excitation input values in the table and then giving minimal SOP expressions for J and for K. https://mallard.cites.uiuc.edu/ECE290/webgrade.cgi?SessionID=mding3_1070311_13325... 3/11/2007 Mallard ECE 290: Computer Engineering I - Spring 2007 - Graded WebQuiz : Sequential... Page 3 of 5 Current Current State Input FF Excitation Q x J K 0 0 1 X 0 1 0 X 1 0 X 1 1 1 X 0 J(Q,x) x J(Q,x) = x'' Enter a minimal SOP Boolean expression K(Q,x) = x'' Enter a minimal SOP Boolean expression K(Q,x) x Your points: 100.00 Option FlipOption 3: A T Flip-Flop Implementation Give a T flip-flop implementation, by providing the excitation input values in the table and then giving a minimal SOP expression for T. Current Current State Input FF Excitation Q x T 0 0 1 0 1 0 1 0 1 1 1 0 T(Q,x) x T(Q,x) = x'' Enter a minimal SOP Boolean expression Your points: 100.00 FlipOption 4: An SR Flip-Flop Implementation Give an SR flip-flop implementation, by providing the excitation input values in the table and then giving minimal SOP expressions for S and for R. Current Current State Input Q x 0 0 1 0 0 1 0 X 1 0 0 1 1 1 X 0 FF Excitation S R S(Q,x) Q'x' S(Q,x) = Q'x' Enter a minimal SOP Boolean expression Qx' R(Q,x) = Qx' Enter a minimal SOP Boolean expression https://mallard.cites.uiuc.edu/ECE290/webgrade.cgi?SessionID=mding3_1070311_13325... 3/11/2007 Mallard ECE 290: Computer Engineering I - Spring 2007 - Graded WebQuiz : Sequential... Page 4 of 5 Your points: 100.00 Implement the Circuit We have already determined the output and the FF excitation functions. A combinational circuit suffices to implement these. Suppose we decide to implement our network using a D flip-flop and that the combinational circuitry to compute D and z uses only AND, OR, and NOT gates. Consider only 2-level AND-OR implementations, corresponding to the equations we derived above. How many AND and OR gates (total) are needed to compute the FF input D and the output z? 6 How many INVERTERS are needed? 1 Note: The state variable Q is available in both complemented and uncomplemented form (because flipflops provide Q' along with Q), but in general the input x is not available already complemented. Suppose instead that we decide to implement our network using a JK flip-flop. How many AND and OR gates (total) are needed to compute the FF inputs J and K and the output z? 3 How many INVERTERS are needed? 1 Draw a circuit to implement the functions determined here. (E.g. try using a D flip-flop and an XOR gate.) Study this circuit. When the input x changes, what other circuit values can change immediately? What changes will need to wait for the clock pulse? Be sure you understand sequential network timing! Item 10: You have filled in all 8 entries in the table correctly. Item 12: You have filled in all 4 entries in the table correctly. Item 14: You have filled in all 8 entries in the table correctly. Item 17: You have filled in all 4 entries in the table correctly. Item 19: You have filled in all 8 entries in the table correctly. You received a raw score of 100% on this question. WebQuiz WebQuiz Grade Summary Raw score Adjusted score Minimum passing score Grade for this submission Cumulative Grade Cumulative 100.00% 100.00% 60.00% 100% 100% https://mallard.cites.uiuc.edu/ECE290/webgrade.cgi?SessionID=mding3_1070311_13325... 3/11/2007 Mallard ECE 290: Computer Engineering I - Spring 2007 - Graded WebQuiz : Sequential... Page 5 of 5 NEW Quiz Mallard Copyright © 1995-2000 Course Content Copyright?1995-2007 Donna J. Brown. All rights reserved. https://mallard.cites.uiuc.edu/ECE290/webgrade.cgi?SessionID=mding3_1070311_13325... 3/11/2007 ...
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This note was uploaded on 06/21/2011 for the course ECE 290 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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