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HW7_Practice_Problems_Solutions

# HW7_Practice_Problems_Solutions - ECE 2030 E,F Practice...

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ECE 2030 E,F Practice Problems - Solutions (1) Textbook #5-14 – The State Diagram for a sequential circuit is given in Fig.5-40 (pg.284). (a) Find the State Table . (b) Make 2-bit state assignments, and write the “encoded” state table . (c) Find the optimized circuit using D flip-flops, NANDs and Inverters. Solution: (a) From the given state diagram, we can construct a state “table” by first listing all the possible combinations of present states and input combinations, then for each of these combinations use the diagram to find the next states and output value(s). P.S. Inputs(X1,X2) N.S. Output(Z) P.S. Inputs(X1,X2) N.S. Output(Z) A 0 0 A 0 C 0 0 A 1 A 0 1 B 0 C 0 1 A 0 A 1 0 B 1 C 1 0 C 1 A 1 1 A 0 C 1 1 C 0 B 0 0 A 0 D 0 0 C 1 B 0 1 A 0 D 0 1 B 1 B 1 0 D 1 D 1 0 B 0 B 1 1 D 1 D 1 1 C 1 (b) We use the most obvious assignment of 2-bit codes (not unique), as follows: A(Q1,Q2)=(0,0) B(Q1,Q2)=(0,1) C(Q1,Q2)=(1,0) D(Q1,Q2)=(1,1) Replace the symbols in the table of part (a) with these values to get : P.S. Inputs(X1,X2) N.S. Output(Z) P.S. Inputs(X1,X2) N.S. Output(Z) 00 0 0 00 0 10 0 0 00 1 00 0 1 01 0 10 0 1 00 0 00 1 0 01 1 10 1 0 10 1 00 1 1 00 0 10 1 1 10 0 01 0 0 00 0 11 0 0 10 1 01 0 1 00 0 11 0 1 01 1 01 1 0 11 1 11 1 0 01 0 01 1 1 11 1 11 1 1 10 1 (c) To optimize the NS and Output logic, we construct three four-variable K-maps using the data in the table from part (b), first listing the minterms for each function: D1 = Q1+(Q1,Q2,X1,X2) = ∑ m(6,7,10,11,12,15)

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HW7_Practice_Problems_Solutions - ECE 2030 E,F Practice...

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