FREQUENCY DIVISION AND COUNTING



Each Flip Flop has its J and K inputs at the 1 level. so that It will change the states (toggle) whenever the signal on its CLK input goe from HIGH to LOW. The clock pulses are applied only to the CLK input of FF Qo. And the important things should be known and noted :

  1. FF Qo toggles on the negative-going transition of each input clock pulse
  2. FF Q1 toggles each time the Qo output goes from HIGH to LOW.
  3. FF Q2 toggles each time Q1 output goes from HIGH to LOW.
  4. Each FF output is a square wave (50 percent duty cycle)




 Each FF divides the frequency of its inpt by 2. using the appropriate number of FFs, this circuit could divide a frequency power of 2. this application of flip-flops is referred to as frequency division.

Counting Operation

In addition to functioning as frequency divider, the circuit in figure 1 also operates as binary counter.



State Transition Diagram



Another way to show how the state of FFs change with each applied clock pulse is to use a state transition diagram as illustrated in figure in this figure.

Each circle represent one possible state as indicated by the binary number inside the circle.
The arrow connecting one circle to another show how one state changes to another as clock pulse applied. We can see which state precedes it and which state follows it.We will use state transition diagrams to help describe, analyze and design counters and other sequential circuits.



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