$39\%$

Microsoft Word $-$ Sample Exam...

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Q$1.$ Up$-$Down Counter Design

$(20$ points$)$

Design a $4-$state synchronous counter with a Reverse input $(R),$ the counter produces the sequence: $0,1,2,3$ then repeats the count when $R=0.$ When $R=1$ the count sequence is $3,2,1,0,$ then repeats. The counter is to be implemented using JK flip$-$flops. The output $Z$ indicates whether the counter is counting UP or DOWN.

a$)$ Complete the state transition table below

b$)$ Derive the input equations for each JK flip$-$flop in minimal sum$-$of$-$products form

c$)$ Show the equation for the output $Z$

$\backslash$table$[[$PS$,$IN$,$NS$,$OUT,JK FFs$,],[Q_1,Q_0,$R$,Q_1^{+},Q_0^{+},$Z$,J_1,K_1,J_0,K_0,],[0,0,0,0,1,0,0,d,1,d,],[0,0,1,1,1,1,,,,,],[,,,,,,,,,,],[,,,,,,,,,,],[,,,,,,,,,,],[,,,,,,,,,,],[,,,,,,,,,,]]$

$J_1=$

$K_1=$

$J_0=$

$K_0=$

$$

$3$