hw06SLN

# hw06SLN - ECE 212 HW Set 6 SOLUTIONS p 1 of 12 ECE 212...

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ECE 212 HW Set 6 SOLUTIONS p 1 of 12 ECE 212 Homework Set 6 SOLUTIONS 1. For the State Transition Diagram shown below: (a) Using a state assignment with three flip-flops, write logic expressions for D2, D1, D0. State Q2 Q1 Q0 S1 0 0 0 S2 0 0 1 S3 0 1 0 S4 0 1 1 S5 1 0 0 S6 1 0 1 S7 1 1 0 (b) Using a state assignment with seven flip-flops, write logic expressions for D1, D2, D3, D4, D5, D6, D7. State Q1 Q2 Q3 Q4 Q5 Q6 Q7 S1 1 0 0 0 0 0 0 S2 0 1 0 0 0 0 0 S3 0 0 1 0 0 0 0 S4 0 0 0 1 0 0 0 S5 0 0 0 0 1 0 0 S6 0 0 0 0 0 1 0 S7 0 0 0 0 0 0 1

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ECE 212 HW Set 6 SOLUTIONS p 2 of 12 (1.) Solution: (a) D2 = ( next state is 100 ) OR ( next state is 101 ) OR ( next state is 110 ) D2 = ( in 011 ) ( A B C ) OR ( in 100 ) OR ( in 011 ) ( A B C ) ' OR ( in 101 ) OR ( in 010 ) ( B C ) ' D2 = ( Q2 ' Q1 Q0 ) ( A B C ) + ( Q2 Q1 ' Q0 ' ) + ( Q2 ' Q1 Q0 ) ( A B C ) ' + ( Q2 Q1' Q0 ) + ( Q2 ' Q1 Q0 ' ) ( B C ) ' Alternate expression [ using ( A B C ) + ( A B C ) ' = 1 ]: D2 = ( Q2 ' Q1 Q0 ) + ( Q2 Q1 ' Q0 ' ) + ( Q2 Q1' Q0 ) + ( Q2 ' Q1 Q0 ' ) ( B C ) '
ECE 212 HW Set 6 SOLUTIONS p 3 of 12 (1.) Solution: (a) D1 = ( next state is 010 ) OR ( next state is 011 ) OR ( next state is 110 ) D1 = ( in 001 ) ( A' ) OR ( in 010 ) ( B C ) OR ( in 101 ) OR ( in 010 ) ( B C ) ' D1 = ( Q2 ' Q1' Q0 ) ( A' ) + ( Q2 Q1 ' Q0 ) ( B C ) + ( Q2 Q1' Q0 ) + ( Q2 ' Q1 Q0 ' ) ( B C ) '

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ECE 212 HW Set 6 SOLUTIONS p 4 of 12 (1.) Solution: (a) D0 = ( next state is 001 ) OR ( next state is 011 ) OR ( next state is 101 ) D0 = (in 000 ) (A) + ( in 001 ) ( A ) OR ( in 010 )(BC) OR (in 011 )( ABC ) ' OR ( in 100 ) D0 = ( Q2 ' Q1' Q0 ' ) (A) + ( Q2 ' Q1 ' Q0 ) (A) + ( Q2 ' Q1 Q0 ' ) ( B C ) + ( Q2 ' Q1 Q0 ) ( A B C ) ' + ( Q2 Q1 ' Q0 ' )
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