Counters are one of the many applications of sequential logic that has a widespread use from simple digital alarm clocks to computer memory pointers. A counter is a collection of flip flops, each representing a digit in a binary number representation (which means each bit, depending on position, means a different number).
One of easier ways to build a circuit is to make a flip flop that controls the activation or switching of the second, and so on. This type of counter is called a ripple counter, since the switching signal propagates from one flip flop to the next as in a wave.
The Ripple Counter
For a simple ripple counter, JK flip flops with both inputs tied to 1 are the best option, since it will toggle state on the clock edge. For simplicity, the falling edge is used and assuming all flip flops start in reset state.
The first FF (Flip Flop) in the sequence gets the its input directly from the variable that needs to be counted. When it transitions from low to high to low again (this last transition generating a falling edge), in other words, when the input pulses, the FF changes to Set.
Since the First FF's output has not made a falling edge transition, the second FF remains Reset.
When another pulse appears at the input, the first FF changes to Reset again, creating a falling edge at its output, which triggers the second FF to transition to the Set state.
Another pulse, the first FF changes to Set; No falling edge at its output, the second FF keeps its state. Yet another pulse (Now four if you have been keeping the count), the first FF goes back to Reset, producing a falling edge; the second FF also goes back to Reset, producing a falling edge at its output that will trigger a third FF and making it Set.
If we assign the value of 1 to the first flip flop, 2 to the second and 4 to the third, we have a 3 bit binary number represented in there. Remember that with binary numbers, we add the values where the binary bit is set to 1.
As you can see, when all the transitions have occurred, the counter ends up with the count of input pulses it has received, representing them in a binary number.
The main drawback of this ripple counter is the fact that as the transition propagates from the first flip flop to the next, all the way to the last one, intermediate numbers are being set at the output, which introduces error and some confusion if a pure counter is needed.
This problem becomes most apparent when all the bits in the counter are set to 1 and another input pulse is applied: The output will be subtracted each time. In a 4 bit ripple counter, the max number that can be represented is 15 (1111), as the transition propagates, intermediate numbers 14 (1110). 12 (1100), 8 (1000) will appear before finally settling into 0 (0000).
