04 Flip-Flops

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Transcript

CHAPTER FOUR flip flops and multi vibrators. We are about to enter into the realms of a subject called combinational. logic and combinational logic has many uses in electronic systems. It's used to carry out the essential arithmetic, not only in computers and calculators, but also in navigation systems, robots and many other types of automatic machinery. However complex such calculations can be, they're all dependent on some basic combinational logic circuits to carry out binary addition and subtraction and registering and saving of information and shifting of information. Some of this arithmetic calculations have already been discussed in our numbering systems.

We are now going to look at such things as shift registers, flip flops, adders, half adders, but we are going to start with looking at multi vibrators and flip flops. The simple gate and combinational logic circuits there is a definite output state for any given input state. Take the truth table for an OR gate for instance, for each of the four combinations of input states 000110 and one one there is a definite unambiguous output state. Whether we're dealing with a multitude of cascaded gates or a single gate the output state is determined by the truth tables and the gates in the circuit and nothing else. However, if we alter this gate circuit so as to give signal feedback from the output to one of the inputs, strange things begin to happen. We know that If A is one, the output must be one as well, such as the nature of an OR gate, any high or one input forces the output high or one.

If A is low zero, however, we cannot guarantee the logic level or state of the output of our truth table as so as shown. Since the output feeds back to one of the OR gate inputs, and we know that any one input to an OR gate makes the output one, this circuit will latch into one output state after a time that a is one. When a is zero, the output could be either zero or one depending on the circuits prior state. The proper way to complete the above truth table would be to insert the word latch in place Question mark, showing that the output maintains the last state when A is zero. Any digital circuit employing feedback is called a multi vibrator. Let's look at one of these multi vibrators is a special multi vibrator called an S bar latch multi vibrator.

The ASR latch multi vibrator has two stable states making it what we call by stable to create an ASR latch, we can wire to NOR gates in such a way that the output of one feeds back to the input of the other and vice versa. Notice that they're that the two outputs are the inverse of each other. In other words, Q. if q is one, then bar Q is going to be zero. And if q is zero, then BB Q is going to be one. So we've indicated the outputs queue and bar queue because they will always when we use the SRR latch for the purposes it was designed for queue will always be the inverse of BB q or the output of one. NOR gate will always be the inverse of the other.

So let's take a look at that. The actual truth table for this arrangement will look like this. You'll notice that if our NSR 00 there are going to be in a lack position which means it will depend on their previous states. We also put down the other three combinations of ASR 01 and one zero and one one. But because we will only use this multi vibrator, when Q and BB q are in the are the inverses of each other the combination of s equals one and r equals one or S equals r equals one is not an option, so it is left out of the consideration. Sometimes this is referred to as an illegal input state.

Let's walk through the logic and see how this s our latch works. Because we are using NOR gates, let's keep the NOR gate truth table handy, and label the inputs of our two NOR gates, A and B. This will help us doing our computation. So let's start with the fact that r is equal to one and S is equal to zero. And I've put the one in the zero on the diagram for RSR latch. One On the AR or the A input of the top NOR gate will output a zero which will feed back to the A input of the bottom NOR gate zero making both inputs zero resulting in the output of the bottom NOR gate one which will feed back to the B input of the top NOR gate one which does not change the output of the NOR gate due to the other input being one as well.

The multi vibrator is stable in this position, which is known as the reset state. Now, let our or the A input becomes zero making RNs inputs zero notice this does not change the output They remain zero and one or latched in the previous state, which is the reset state. Okay, having done that, let's look at the S equals one and r equals zero input to our ASR latch. And I've written in the inputs zero and one on our diagram. One on the s or the B input of the bottom NOR gate will output a zero which will feed back to the B input of the top NOR gate zero, making both inputs zero resulting in the output of the top NOR gate one, which will feed back to the input of the bottom NOR gate one, which does not change the output of the night. gait due to the other input being one.

The multi vibrator is now stable in this position which is known as the set state. Now, let the s or the B input of the bottom NOR gate become zero making both S and R inputs zero. Notice this does not change the output they remain one and zero or latched in the previous state or the set state. By definition, a condition of Q equals one and bar q equals zero is a set condition that condition of Q equals zero and not Q equal to r bar Q equal to one is a reset state. These terms are universal in describing The output states of a multi vibrator circuit in semiconductor form SSR latches come in pre packaged units so that they don't have to be built from individual gates. And the ASR gate would be symbolized like this where you have only two inputs an S nr with a Q and A BB q output, the BB q output is denoted by the little bubble on the end of the the wire coming off it, but the states are indicated that they are the inverse of each other.

And of course the the fact that we might we could possibly have SNR equal to one. We don't use that state so we've actually shaded that out or that's what we call the illegal state for NSR latch. It is sometimes useful in logic circuits to have a multi vibrator which changes states over When certain conditions are met, regardless of the SNR input states, the conditional input is called an enable, and it is symbolized by the letter E. In our diagram here we can see that we have now two AND gates feeding into our s our latch, and two of the inputs to each of those n gates are the Enable circuit. Let's have a look at how it works. The truth table for this circuit arrangement is given here, when the E input is zero, the output of the two n gates are forced to zero regardless of the states of either s or R. Consequently, the circuit behaves as though sn r were both zero latching the Q and the Q not outputs to their last steaks only When the Enable input is activated, in other words is a one will the latch respond to the SNR inputs.

Once again these multiple vibrator circuits are available in pre packaged semiconductor devices and are symbolized by these, the truth table will still describe the outputs. But now we have basically three inputs an SNR and an enable E. Since the Enable input on a gated SSR latch provides a way to latch the cue and the bar q or not q outputs without regard to the status of S or R. We can eliminate one of those inputs to create a multi vibrator latch circuit with no illegal input states. Such a circuit is called a D latch and Internal circuitry would look like this. Note that the our input has been replaced with a compliment inversion of the old s input and the S input has been renamed D. As with a gated s our latch the D latch will not respond to a signal a SIG signal input.

If the Enable input is zero, it simply stays latched in the last state, when the Enable input is one however, the Q output will follow the D input. Since the our input of the ASR circuitry has been done away with this latch has no invalid or illegal state Q and not Q are always opposite to each other. And like both the S R and the gated SSR latches the D latch circuit can be found. As its own pre pre packaged circuit circuit, complete with these standard symbols, and the logic of this circuit is described by this truth table. In many digital applications, however, it is desirable to limit the responsiveness of a latch circuit to be a very short period of time instead of the entire duration that the Enable input is activated. One method of enabling a multi vibrators circuit is called edge triggering, where the circuits data inputs have control only during the time that the Enable input is transitioning from one state to the other.

In this case, we've written a time display curve for the various states of the input Have a deal of a D flip flop, you have a D input and an enable input. And the Q and the q naught are shown on the bottom two lines over a period of time. The outputs only respond to the D input during that brief moment of time when the Enable signals changes or transitions from a low to a high. This is known as positive edge triggering. And if you look at our diagram, the enable signal is edge triggering when here but the D is zero, so the Q output is still zero. In this we still have E as a going positive from negative and its edge triggered by D is still zero, so Q is still zero.

However, in the final stage when you get an edge trigger for IE, it is edge trigger when D is one. So consequently, the the latch will flip and the Q will change from zero to one and the bar q will change from one to zero. There is also such a thing as a negative edge triggering as well and it produces the following response to the same input signals and we'll see that in the next slide. Whenever we enable the multi vibrator circuit on a transitional edge of a square wave enable signal we call it a flip flop instead of a latch. Consequently, the edge triggering as our circuit is more properly known as an S, our flip flop and an edge triggered D circuit. As a D flip flop, the enable signal is ready name to be a clock signal.

Also we refer to the data inputs as R and D, respectively of these flip flops as synchronous inputs, because they have effect only at a time of the clock pulse transition, thereby synchronizing any output changes with that clock pulse. showing here is how negative a edge triggering would work in the case of a D flip. And again, we have our our two inputs, the the D input and the Enable input shown over time, and we have the outputs of what the flip flop would look like as well. So we're starting out with q being in the zero state and BB q being in the one state and as we move along, D is pulsing, positive or negative, but the information from D will only get transferred to the Q output and the BB q output when he is transitioning negatively in other words going down. For example, at this location, the enable signal is going from positive one to a zero that enables the D latch or sorry the D flip flop in this case to transfer its information to the Q output, so, the Q output will flip and it will go from zero to one and the D, the BB q will go from a one to a zero.

At this stage, the next negative going pulse of the Enable edge triggering happens when D is at a zero. So, the Q will change along with the D because it has been enabled by the negative going pulse of the Enable. So, input. And and in the last instance here, we get another negative going pulse from the Enable, but the D itself is zero, so we don't get any flipping of the of the output because Q is already in the zero state. Pulse detectors are built on the front end of bulky vibrators, we can show it attached to the enabled input of the latch to turn it into a flip flop. In this case, the circuit is an S our flip flop.

Looking at the truth table, only when the clock signal C is transitioning from a low to a high and it's indicated by kind of a status symbol. So this is a transitioning from low to high. Is the circuit responsive to the ASR inputs for any other condition of the clock signal x, the circuit will stay latched. The block symbols for flip flops are slightly different than that of their respective latch counterparts. The triangle symbol next to the clock inputs tells us that these are edge trigger devices and consequently, that these are flip flops rather than latches. These symbols are positive edge triggering, that is the clock on the rising edge low to high transition of the clock signal.

Negative edge triggering devices are symbolized like this with a bubble on the clock input line. Both these flip flops will clock on the falling edge high to low transition of the clock signal. Another variation on the theme of bi stable multi vibrators is the JK flip flop. Essentially, this is a modified version of the ASR flip flop with no invalid or illegal output states. This circuit works in this way as shown by the truth table if the J k inputs are the inverse of each other that is if j for instance is equal to one and k is equal to zero, or j equal to zero and k is equal to one and that clock signal happens the J and the K logic is transferred or shifted to the Q and the BB q outputs. If the J k inputs are zero This flip flops stays latched in whatever position it was before.

When both J and K inputs are one however, something unique happens in this case, on the next clock pulse the outputs will be switched or toggled. If q was equal was one and not Q is zero, then they will toggle such that now q will switch to zero and not Q will switch to one. The next clock pulse toggles the circuit in the other direction, and Q and BB q will change states. So as long as J and K inputs are one, every clock pulse toggles the output from the previous state to the inverse state and then back again and then back again as long as the triggering impulses are coming. The block symbols for a JK flip flop is a whole lot less frightening than its internal circuitry. The truth table still holds true.

And just like the ESR and the D flip flop, the JK flip flop comes in two clock various varieties, the negative and the positive edge triggering. Remember that the truth table that you see in front of you here is the one for the positive edge triggering. So in subsequent chapters, we'll see how these flip flops and multi vibrators can be put to use in combinational logic circuits for now. We've just seen how they work. And that completes chapter four

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