ECE251 hw10 - sol

# ECE251 hw10 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT...

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NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT. OF ELECTRICAL & COMPUTER ENGINEERING ACADEMIC YEAR 2008-2009 SEMESTER 1 ECE251 DIGITAL DESIGN S OLUTION HW10 1. We create the state partitions from the given state table. PS NS, Z x = 0 x =1 A A,0 B,0 B B,0 C,0 C C,0 D,0 D D,0 A,1 E E,0 F,0 F B,0 G,0 G G,0 H,0 H D,0 E,1 ) ( 0 ABCDEFGH P = ) )( ( 1 DH ABCEFG P = ) )( )( ( 2 CG DH ABEF P = ) )( )( )( ( 3 BF CG DH AE P = ) )( )( )( ( 4 BF CG DH AE P = So, the reduced machine has 4 states. We rename the states as: ) ( ) ( ) ( ) ( DH CG BF AE = = = = δ γ β α The state table of the minimal machine is: 1

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P S NS, Z x =0 x =1 α α ,0 β ,0 β β , 0 γ ,0 γ γ ,0 δ ,0 δ δ ,0 α ,1 2. We use the following state assignment: State 2 1 Q Q α 00 β 01 γ 10 δ 11 State table: P S NS, Z x =0 x =1 00 00, 0 01,0 01 01, 0 10,0 10 10, 0 11,0 11 11, 0 00,1 Excitation and output table: K-maps and Boolean equations: 2 PS 2 1 Q Q 1 1 R S 2 2 R S Z x = 0 x = 1 x =0 x =1 x =0 x =1 00 0 φ 0 φ 0 φ 10 0 0 01 0 φ 10 φ 0 01 0 0 10 φ 0 φ 0 0 φ 10 0 0 11 φ 0 01 φ 0 01 0 1
00 01 11 10 0 1 00 01 11 10 0 1 00 01 11 10 0 1 00 01 11 10 0 1 2 1 Q Q 2 1 Q Q 2 1 Q Q 2 1 Q Q x x x x 0 0 φ φ 0 0 1 φ x Q Q S 2 1 1 = φ 0 0 1 00 01 11 10 0 1 2 1 Q Q x x Q Q R 2 1 1 = 0 0 φ φ 1 1 0 0 φ φ 0 0 x Q S 2 2 = φ 0 0 1 1 0 0 x Q R 2 2 = 1 0 0 0 0 0 0 0 x Q Q Z 2 1 = φ Circuit implementation: Q Q SET CLR S R Q Q SET CLR S R 1 2 x Ck Fig. 1. Circuit implementation Z 3. The stable states are circled: 3

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00 01 11 00 01 10 10 11 AB xy 00 01 10 11 Fig. 2. The stable states 10 00 00 01 01 11 11 10 00 00 10 10 XY 4. We have the following cases: (a) The change of A
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