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Up until now, our digital circuits have been strictly combination -- they take inputs and react to them. While they are capable of complex calculations, they lack the ability to remember what they've done. This lack of memory severaly restricts the capabilities of the circuits we can design. The flip-flop is the basic unit of digital memory. A flip-flop can remember one bit of data. Sets of flip-flops are called registers, and can hold bytes of data. Sets of registers are called memories, and can hold many thousands of bits, or more. The basic flip-flop circuit is the classic set of cross-coupled NAND gates. Since nobody builds flip-flops from the gate level anymore, we'll skip past this level of analysis, and move straight into the chips we'll actually use. But if you're interested,  The Art of Electronics  devotes many pages to the inner workings of flip-flops, from the cross coupled NAND's on up. D-flops One of the most common kinds of flip-flops (or,

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 : FF Qo toggles on the negative-going transition of each input clock pulse FF Q1 toggles each time the Qo output goes from HIGH to LOW. FF Q2 toggles each time Q1 output goes from HIGH to LOW. 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