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Design a mod 5 synchronous up counter using J-K flip flop

Mumbai University > COMPS > Sem 3 > Digital Logic Design and Analysis

Marks: 10 M

Year: May 2015

1 Answer
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Step 1:

Determine the number of flip flop needed

Flip flop required are

$2^n ≥ N$

Mod 5 hence N=5

$\therefore 2^n \underline{\gt} N \\ \therefore 2^n \underline{\gt} 5 \\ N=3 \hspace{0.2cm} \text{i.e. 3 flip flop are required}$

Step 2:

Type of flip flop to be used: JK flip flop

Step 3:

1) Excitation table for JK flip flop

$Q_n$ $Q_{n+1}$ J K
0 0 0 $\times$
0 1 1 $\times$
1 0 $\times$ 1

Now, we can derive excitation table for counter using above table as follows:

2) Excitation table for counter

enter image description here

Step 4

K-map simplification

For $J_C$

enter image description here$J_c=Q_BQ_A$

For $K_C$

enter image description here$K_C=1$

For $J_B$

enter image description here$J_B=QA$

For $K_B$

enter image description here$K_B=QA$

For $J_A$

enter image description here$J_A=\overline{Q}_C$

For $K_A$

enter image description here$K_A=1$

Step 5 Logic Diagram

enter image description here

Step 6: Timing Diagram

enter image description here

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