hw3_soln_Sp2010

# hw3_soln_Sp2010 - Q A Q B ¯ Q C S = ¯ Q C ¯ Q D ¯ Q B...

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ECE 561 (Sp 2010) Homework #3 – Solutions 1. State Diagram: X X INIT X INIT INIT X X X X X b c d g h f X X INIT INIT a X X e Z X X 2. (a) State Table: ( D A ) ( D B ) Q A Q B S 1 S 0 Q A Q B 0 0 0 0 0 0 0 0 0 1 R 0 0 0 1 0 0 L 0 0 1 1 A B 0 1 0 0 0 1 0 1 0 1 R 0 0 1 1 0 1 L 0 1 1 1 A B 1 0 0 0 1 0 1 0 0 1 R 1 1 0 1 0 0 L 1 0 1 1 A B 1 1 0 0 1 1 1 1 0 1 R 1 1 1 1 0 1 L 1 1 1 1 A B Equations: D A = Q A ¯ S 1 ¯ S 0 + RIN ¯ S 1 S 0 + A S 1 S 0 + Q B S 1 ¯ S 0 D B = Q B ¯ S 1 ¯ S 0 + Q A ¯ S 1 S 0 + B S 1 S 0 + LIN S 1 ¯ S 0 The logic diagram follows from these equations.

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(b) t s S 1 ,S 0 65 ns (3x15 + 20) A,B,RIN,LIN 50 ns (2x15 + 20) t h S 1 ,S 0 ,A,B,RIN,LIN -25 ns (5 - 2x15) 0 CLR Q 40 ns CLK Q 40 ns f MAX 11.1 Mhz (delay = 40 + 2x15 + 20 = 90 ns) (c) Equations: D A = Q A ¯ S 1 ¯ S 0 + RIN ¯ S 1 S 0 + A S 1 S 0 + Q B S 1 ¯ S 0 D B = Q B ¯ S 1 ¯ S 0 + Q A ¯ S 1 S 0 + B S 1 S 0 + Q C S 1 ¯ S 0 D C = Q C ¯ S 1 ¯ S 0 + Q B ¯ S 1 S 0 + C S 1 S 0 + Q D S 1 ¯ S 0 D D = Q D ¯ S 1 ¯ S 0 + Q C ¯ S 1 S 0 + D S 1 S 0 + LINS 1 ¯ S 0 3. Finite State Machine See the fnal page o± this solution. 4. State Table: Q A Q B Q C Q D Q A Q B Q C Q D S 1 S 0 RIN LIN 0 0 0 0 1 0 0 0 0 1 1 x 0 0 0 1 0 0 0 0 0 1 0 x 0 0 1 0 0 0 0 0 1 1 x x 0 0 1 1 0 0 0 1 0 1 0 x 0 1 0 0 0 0 0 0 1 1 x x 0 1 0 1 0 0 0 0 1 1 x x 0 1 1 0 1 1 0 1 1 0 x 1 0 1 1 1 0 0 1 1 0 1 0 x 1 0 0 0 1 1 0 0 0 1 1 x 1 0 0 1 0 0 0 0 1 1 x x 1 0 1 0 0 0 0 0 1 1 x x 1 0 1 1 0 1 1 1 1 0 x 1 1 1 0 0 0 1 1 0 0 1 0 x 1 1 0 1 1 0 1 1 1 0 x 1 1 1 1 0 0 0 0 0 1 1 x x 1 1 1 1 0 0 0 0 1 1 x x Equations: A = B = C = D = 0 CLR = 0 LIN = 1 RIN = ¯ Q B ¯ Q D S 1 = Q A Q D + Q C ¯ Q D + ¯
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Unformatted text preview: Q A Q B ¯ Q C S = ¯ Q C ¯ Q D + ¯ Q B ¯ Q D + ¯ Q A Q D + ¯ Q B ¯ Q C + Q A Q B Q C Problem 3 - Diagram...
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hw3_soln_Sp2010 - Q A Q B ¯ Q C S = ¯ Q C ¯ Q D ¯ Q B...

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