Solving Mod 13 Ripple Counter with D Flip Flop

[d_b]

Homework Statement

I'm working on this problem but everytime I tried to walk through my answer it doesn't seem right.

I wanted to built a ripple counter, up counter with mod 13 using D flip flop.

Homework Equations

present state ABCD - 0000-->1101
next state ABCD - 0001-->0000

Q(t+1) = Dq

The Attempt at a Solution

I first built the state diagram going from 0000 to 1101 then back to 0000.

Now the textbook said to use take the compliments of the output from the D flip flop. So what I did I took the compliment of the output(next state) and the unused state (14 and 15 as don't care) and by k-map i constructed a formula for the 4 D-FF. However as soon as I hit 13(1101) it will not go back to 0000.

The other approach is: I took the output from the next state and the unsued state(1110 and 1111 as don't care states), using k-map again i constructed a formula for the sum of product of the 4 D-FF. But agian it will not go from 1101 to 0000.

Then I redo it by using complements output of the next state with k-map to built the formula for the FFs without the unused state and it still doesn't work.

I redo it agian by using output of the next state with k-map to built the formula for the FFs without the unused state and still doesn't work.

I know that I'm doing something wrong during the process, however I'm not sure howelse to built this FFs.

 

[d_b]

oh...this is not a homework either, its my exam review questions...