4,967 views
23 votes
23 votes
Design a synchronous counter to go through the following states:$$1, 4, 2, 3, 1, 4, 2, 3, 1, 4 \dots $$

3 Answers

Best answer
28 votes
28 votes

Sequence given is as

$ 1,4,2,3,1\ldots$

From the given sequence of states we can design the state table and Suppose we are using T-FF for sequential circuit of counter.$$\small \begin{array}{|ccc|ccc|ccc|}\hline
\rlap{\textbf{Present State}}&  &  & \rlap{\textbf{Next State}} &  &  & \rlap{\textbf{FF Inputs}} &  &   & \\\hline \;\; A\;\;  &\;\; B\;\; &\;\; C \;\; & A^{+} & B^{+} & C^{+} & T_{A} & T_{B} & T_{C} \\\hline 0 & 0 & 0 & x& x & x & x & x  & x  \\\hline 0 & 0 & 1 & 1&0 &0 &1 &0 & 1  \\\hline 0 & 1 & 0 & 0&1 &1 &0 &0 & 1  \\\hline 0 & 1 & 1 & 0&0 &1 &0 &1 &0  \\\hline 1 & 0 & 0 & 0&1&0 &1 &1 & 0   \\\hline 1 & 0 & 1 & x& x & x & x & x  & x   \\\hline 1 & 1 & 0 & x& x & x & x & x  & x   \\\hline 1 & 1 & 1 & x& x & x & x & x  & x  \\\hline  \end{array}$$From the above table, we will find the equation of $T_A$, $T_B$ and $T_C$

edited by
2 votes
2 votes

Using D-FlipFlops

An Bn Cn An+1 Bn+1 Cn+1
0 0 0 X X X
0 0 1 1 0 0
0 1 0 0 1 1
0 1 1 0 0 1
1 0 0 0 1 0
1 0 1 X X X
1 1 0 X X X
1 1 1 X X X

 

After minimizing An+1, Bn+1, Cn+1 using K-Map

An+1 = Bn’C

Bn+1 = Cn’

Cn+1 = B

 

 

0 votes
0 votes

Generally synchronous counter are designed by using D- flip flop and asynchronous counter are designed by using T- flip flop. So here counter designed by using D flip-flop

Related questions

31 votes
31 votes
3 answers
1
24 votes
24 votes
1 answer
2
Kathleen asked Sep 25, 2014
8,166 views
The function represented by the Karnaugh map given below is$A.B$$AB+BC+CA$$\overline{B \oplus C}$$A.BC$
31 votes
31 votes
2 answers
3
Kathleen asked Sep 25, 2014
8,094 views
The octal representation of an integer is $(342)_8$. If this were to be treated as an eight-bit integer in an $8085$ based computer, its decimal equivalent is$226$$-98$$7...
42 votes
42 votes
4 answers
4
Kathleen asked Sep 25, 2014
9,977 views
What happens when a bit-string is XORed with itself $n$-times as shown:$\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]$complements when $n$ is evenco...