Experiment 10 - The "False" Synchronous 4-bit Counter

Can you build a synchronous n-bit counter, by expanding the chain of flip-flops? What has worked so well in the case of asynchronous counters, no longer works for synchronous counters...

Take a look at the circuit diagram. You realize that the synchronous 2-bit counter has been extended by two flip-flops...

Circuit diagram "false" 4-bit synchronous counter.

Illustration states "false" 4-bit synchronous counter.

The circuit does not count as expected! Actually the "false" synchronous 4-bit counter passes through only 8 states and not the 16 states you would expect...

Circuit "false" 4-bit synchronous counter. (Enlarge)

You can easily understand the 8 states, by going through the circuit with the logic of a T-type flip-flop in mind...

But how do you build a working synchronous 4-bit counter...?