Chapter 9 - Chapter 9 Problem Solutions 9.1. Excitation and...

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- 9.1 - Chapter 9 Problem Solutions 9.1. Excitation and output expressions: Y 1 = x 1 x - 2 + x 2 y 1 Y 2 = x 2 y 1 + x - 2 y 2 z = y 2 Excitation/transition table: State table: Present state Next state Output (z) Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 00 A A AC A 0 0 0 0 01 B B A D A 1 1 1 1 10 C A D C D 0 0 0 0 11 D B D D D 1 1 1 1
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- 9.2 - 9.1. (continued) Flow table: Present state Next state Output (z) Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 A A AC A 0 0 - 0 B B A D - 1 - - - C A - C D - - 0 - DB D D D - 1 1 1 Flow diagram:
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- 9.3 - 9.2. Excitation and output expressions: Y 1 = x 1 y 1 + x 1 x - 2 y - 2 Y 2 = x 1 x - 2 y 1 + x - 1 x 2 y 1 y 2 z = x 1 y 1 y - 2 + x 1 x - 2 y 1 Excitation/transition table: State table: Present state Next state Output (z) Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 00 A A AC A 0 0 0 0 01 B A A A A 0 0 0 0 10 C A A D C 0 0 1 1 11 D A B D C 0 0 1 0
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- 9.4 - 9.2. (continued) Flow table: Present state Next state Output (z) Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 A A AD A 0 0 - 0 C - A D C - - - 1 D A - D C - - 1 - Flow diagram:
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- 9.5 - 9.3. Excitation and output expressions: S 1 = x - 1 x - 2 Q 2 + x 2 Q - 1 Q - 2 R 1 = x - 2 Q - 2 + x 1 Q 1 Q - 2 S 2 = x 1 Q - 1 R 2 = x - 1 x 2 z = x - 1 x - 2 Q 2 + Q 1 Q 2 Excitation table: Present state (Q 1 Q 2 ) Excitation (S 1 R 1 ,S 2 R 2 ) Output (z) Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 00 01,00 10,01 01,10 10,10 0000 01 10,00 00,01 00,10 00,10 1000 10 01,00 00,01 01,00 01,00 11 10,00 00,01 00,00 00,00 1111 Transition table:
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- 9.6 - 9.3. (continued) State table: Present state Next state Output (z) Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 00 A A C B D 0 0 0 0 01 B D A B B 1 0 0 0 10 C A C A A 0 0 0 0 11 D DC D D 1 1 1 1 Flow table: Present state Next state Output (z) Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 A A C B - 0 - - - B D C B B - - 0 0 CA C - D - 0 - - D D D 1 - 1 1 Flow diagram:
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- 9.7 - 9.4. Primitive flow table: Present state Next state Output (z) State definition Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 x 1 =x 2 as a result of an x 1 change A A C D - 0 - - - x 1 =x 2 as a result of an x 2 change B B C D - 1 - - - x 1 =0, x 2 =1 CB C - E - 0 - - x 1 =1, x 2 =0 D A - D F - - 0 - x 1 =x 2 as a result of an x 1 change E - C D E - - - 0 x 1 =x 2 as a result of an x 2 change F - C D F - - - 1 This is an input-restricted flow table. Using the reduction procedure of Sec. 9.5, the processed implication table is: The maximal compatible sets are: {A,D,F}, {B,C,E}, {A,E}, {B,F} Minimal collection of maximal compatible sets is: {A,D,F}, {B,C,E}
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- 9.8 - 9.4. (continued) Minimal-row flow table: Present state Next state Output (z) Input state (x 1 x 2 ) Input state (x 1 x 2 ) 00 01 10 11 00 01 10 11 {A,D,F}:  0-01 {B,C,E}:  10-0 Using the reduction procedure of Sec. 9.6, the processed implication table is: No equivalent stable states.
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Chapter 9 - Chapter 9 Problem Solutions 9.1. Excitation and...

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