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## Q: MOD 6 Counter

Q- Can we design a MOD-6 counter using the above method?

Ans:  We firstly draw the state diagram

And now we draw the table to represent the desired output of the combinational circuit to reset FFs as:

Q2          Q1          Q0                          OUTPUT

0              0              0                              1

0              0              1                              1

0              1              0                              1

0              1              1                              1

1              0              0                              1

1              0              1                              1

1              1              0                              0

1              1              1                              0

And using K-map we get the combinational circuit as

And the complete circuit is as: Categories

## USING K-MAPS to design counter

Q- Design MOD-3 ripple counter using (a) Observing outputs (b) K-maps to design the circuit.

Ans: (a)We can design the MOD 3 counter using 2 FFs as 3 is less than 4 i.e. 22 and greater than 2. We can see directly that as we have to reset the counter only after 2 i.e. when output is 3 we reset the counter and hence we need to reset only when we have Q0= 1 & Q1=1. Now firstly design MOD-4 counter using 2 FFs and then take NAND of Q0 & Q1 and feed the output to CLEAR of both FFs.

(b) We firstly draw state diagram of the counter required as:

And we have the general circuit to design the other than MOD 2 n then we have the general circuit as

And now we draw a table to list the different input combinations to Combinational circuit and their corresponding output as:

Q1          Q0                          OUTPUT of reset logic

0              0                              1

0              1                              1

1              0                              1

1              1                              0

And using K-map as

And hence we get the whole circuit for MOD-3 counter as Categories

## Conversion: D to RS flip-flop

We first write the truth table for required Flip-flop i.e. RS FF

Now we write the excitation table of given FF i.e. D flip-flop as

Now we combine two tables to get the combinational circuit as:

Now we design the combinational circuit to convert J, K to corresponding R, S

K-map for D input:

And we get the circuit to convert D to SR FF:

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## Conversion: RS to JK flip-flop

We first write the truth table for required Flip-flop i.e. JK FF

Now we write the excitation table of given FF SR flip-flop as

Now we combine two tables to get the combinational circuit as:

Now we design the combinational circuit to convert J, K to corresponding R, S

K-map for S input:

K-map for R input:

So we get the circuit to convert RS FF to JK FF:

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## Conversion: RS to D flip-flop

Let’s first now derive the D flip-flop from RS flip-flop which we have already done:

We first write the truth table for required D flip-flop as

Now we write the excitation table of given FF SR flip-flop as

Now we need to make a arrangement so that we manipulate input D to inputs R, S such that we get the same output with RS FF as that of D FF. So we combine the two tables given above with same outputs in the same row:

Now we design the combinational circuit to convert D input to SR inputs using K-map as:

K-map for S input:

K-map for R input:

Hence we convert the SR FF to D FF as: