# hw3 - CS2204 DIGITAL LOGIC STATE MACHINE DESIGN HOMEWORK...

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HOMEWORK III CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2010 Polytechnic Institute of NYU Page 1 of 18 Handout No : 9 February 23, 2010 DUE : March 11, 2010 READ : Related portions of Chapters VII and VIII ASSIGNMENT : There are three questions. Solve all homework and exam problems as shown in class and past exam solutions. 1) Consider the following sequential circuit : Analyze the sequential circuit in the style shown in class. This question is identical to textbook problem 7.12 except that FF y 2 is renamed y 0 . Note that this is a Moore circuit since the only sequential circuit output, z, is not a function of input x. Also, this is a non-finite memory circuit since the FFs do not form a shift register. 2) Consider the following sequential circuit : Analyze the sequential circuit in the style shown in class. Since FF y 1 output is sequential circuit output z 1 and FF y 0 output is sequential circuit output z 0 , this circuit is also a Moore circuit : The sequential circuit outputs, z1 and z0, are not a function of input x. Finally, this is a non-finite memory circuit since the FFs do not form a shift register. D C Q Q D C Q Q y 0 y 1 y 1 y 0 clock clock seq. circuit x z clock x y 1 y 1 y 0 y 0 y 0 y 1 y 0 z J K C Q Q J K C Q Q x z 1 y 0 y 1 x y 0 y 1 z 0 clock clock seq. circuit x z 1 z 0 clock x x y 1 y 1 y 0 y 0

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Polytechnic Institute of NYU Page 2 of 18 CS2204 Handout No : 9 February 23, 2010 3) Consider the following sequential circuit : Analyze the sequential circuit in the style shown in class. Note that there are 2 (two) inputs hence there are four sets of next state columns. Is this sequential circuit a Moore or Mealy circuit ? Why ? RELEVANT QUESTIONS AND ANSWERS Q1) Consider the following sequential circuit : Analyze the sequential circuit in the style shown in class. Is this circuit is a Mealy or Moore circuit ? Why ? FF y 1 is the most significant FF. The FF y 1 output is sequential circuit output z 1 and the FF y 0 output is sequential circuit output z 0 . A1) a) Flip-flop input and sequential circuit output equations : J 1 = x y 0 D 0 = x y 1 + x y 0 + x y 0 z 1 = y 1 K 1 = x y 0 z 0 = y 0 Since sequential circuit outputs z 1 and z 0 do not depend on x, this is a Moore circuit. Q Q C T x1 clock Most significant x0 Y y 1 z1 z0 msb Q Q C T y 0 x1 z1 z0 clock clock x0 x1 x0 FF y 0 y 0 x0 x1 x1 x0 x1 x0 J K C Q Q D C Q Q z 1 y 0 y 1 y 0 y 1 z 0 clock clock seq. circuit x z 1 z 0 clock x x x y 0 x Most Significant FF y 0 x
Polytechnic Institute of NYU Page 3 of 18 CS2204 Handout No : 9 February 23, 2010 b) Next flip-flip output (next state) equations : Q2) Consider the sequential circuit below with two inputs and one output. Its transition table (excitation table) is also given. Continue the analysis. The labeling of FFs is the opposite of our convention, but, we will keep it : y 1 = J 1 y 1 + K 1 y 1 = (x y 0 )y 1 + (x y 0 )y 1 = x y 1 y 0 + [(x + y 0 )]y 1 = x y 1 y 0 + x y 1 + y 1 y 0 y 0 = D 0 = x y 1 + x y 0 + x y 0 c) The excitation table : y 1 y 0 x = 0 x =1 z 1 z 0 x=0 x=1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 y 1 y 0 d) The state table : PS x=0 x=1 q0 q1 q0 0 q1 q2 q1 1 q2 q3 q2 2 q3 q1 q3 3 NS OUT q0/0 q1/1 q2/2 q3/3 0 0 0 1 e) The state diagram : 1 1 1 f)

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hw3 - CS2204 DIGITAL LOGIC STATE MACHINE DESIGN HOMEWORK...

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