# Slide Set 7. for ENEL 353 Fall Steve Norman, PhD, PEng. Electrical & Computer Engineering Schulich School of Engineering University of Calgary

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1 Slide Set 7 for ENEL 353 Fall 216 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 216

2 SN s ENEL 353 Fall 216 Slide Set 7 slide 2/45 Contents Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

3 SN s ENEL 353 Fall 216 Slide Set 7 slide 3/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

4 SN s ENEL 353 Fall 216 Slide Set 7 slide 4/45 Combinational versus Sequential Logic This is review: The outputs of a combinational logic circuit depend only the current values of its inputs. The outputs of a sequential logic circuit depend on the history of its input values. We ve just seen that the above definition of combinational logic is very slightly untrue, due to very tiny delays. However, sequential logic is totally different. Outputs of sequential logic circuits may depend on the history of input values indefinitely far back in the past minutes, hours, or days, not just picoseconds.

5 SN s ENEL 353 Fall 216 Slide Set 7 slide 5/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

6 SN s ENEL 353 Fall 216 Slide Set 7 slide 6/45 SR latches Here are two ways to build an SR latch, perhaps the simplest sequential circuit element: NOR-based R NAND-based S S N R N Notice that it s possible to wire together combinational devices in ways that produce sequential devices! Harris & Harris use and as names of outputs, but I prefer and N because as we ll soon see it s not always true that N = NOT().

7 SN s ENEL 353 Fall 216 Slide Set 7 slide 7/45 Static analysis of the SR latch We ll look at the NOR-based circuit. (Analysis of the NAND-based circuit is very similar.) R = (R + N) N = (S + ) S N depends on N, and N depends on. This is a system of two Boolean algebra equations in two unknowns! For all four possible combinations of R and S, let s solve for and N.

8 SN s ENEL 353 Fall 216 Slide Set 7 slide 8/45 Dynamic behaviour of a NOR-based SR latch 1 S 1 R 1 1 N useful behaviour problematic behaviour???????? A pulse on S or R is a transition from to 1, followed later by a transition from 1 to. Let s make some notes about useful and problematic behaviour of the SR latch.

9 SN s ENEL 353 Fall 216 Slide Set 7 slide 9/45 The SR latch is an example of a bistable circuit A bistable circuit is one that will sit in either one of two stable states. We ve just seen that an SR latch is bistable when S = R = : either (, N) = (,1) or (, N) = (1,). It s important to understand that if there are no pulses on S or R, the state of an SR latch will persist as long as the circuit is powered up. When S = R =, the state will not spontaneously flip between (, N) = (,1) and (, N) = (1,) (unless the latch is affected by severe electrical noise). To understand why the state is stable when S = R =, you need to study the pull-up and pull-down networks of the gates that make up an SR latch. That is not an ENEL 353 topic.

10 SN s ENEL 353 Fall 216 Slide Set 7 slide 1/45 Symbols for SR latches It s less important to know what is going on inside an SR latch (NOR gates, NAND gates, inverters and/or other devices) than it is to know its behaviour as a black box. (Black box: You can play with its inputs and observe its outputs, but you can t look inside it.) Here are two symbols, one from our course textbook, and another from an author named Wakerly... S S R R N (Wakerly s Digital Design book is very good, but for a beginner, reading it may be somewhat like trying to drink from a firehose.)

11 SN s ENEL 353 Fall 216 Slide Set 7 slide 11/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

12 SN s ENEL 353 Fall 216 Slide Set 7 slide 12/45 Clock signals A clock signal in a digital circuit is a periodic square wave : 1 t H t L T C time T C is the period of the clock, also called the cycle time. The clock frequency f C is related to the period as f C = 1/T C. If the frequency of a clock is 2.5 GHz, what is its period? The duty cycle is defined as (t H /T C ) 1%. Usually t H = t L =.5T C, so the duty cycle is 5%, but that s not true for all clock signals.

13 SN s ENEL 353 Fall 216 Slide Set 7 slide 13/45 Clock signals and sequential logic systems In the most common kind of sequential circuit, a common clock signal is supplied to all of the D latches and/or D flip-flops in the circuit. (D latches and D flip-flops are important sequential logic components that will be presented very soon.) In digital integrated circuit design, distributing a common clock signal to all the latches and flip-flops in the circuit is just as important as making sure V DD and ground are connected to all combinational and sequential elements.

14 SN s ENEL 353 Fall 216 Slide Set 7 slide 14/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

15 SN s ENEL 353 Fall 216 Slide Set 7 slide 15/45 uick review of the SR latch, part 1 R S N S R N A pulse on S sets the state drives it to 1. A pulse on R resets the state drives it to. If there are no pulses on S or R, the state maintains its value as long as the circuit is powered up. In normal operation, N =.

16 SN s ENEL 353 Fall 216 Slide Set 7 slide 16/45 uick review of the SR latch, part 2 R S N Asserting S and R at the same time (in other words, making S = R = 1) should be avoided. When S = R = 1, it s possible that = N. For the NOR-based SR latch, we saw that when S = R = 1, = N =. (For a NAND-based SR latch, when S = R = 1, it turns out that = N = 1.) Behaviour of an SR latch when S and R make 1 transitions at nearly the same time is unpredictable.

17 SN s ENEL 353 Fall 216 Slide Set 7 slide 17/45 The D latch A D latch has two input wires. One of them is called D, for data. The other is usually called CLK, and is usually connected to a clock signal. One way to make a D latch is with an SR latch... CLK R D S N Why is it safe to label the D latch outputs as and, rather than and N as was done for the SR latch?

18 Behaviour of a D latch slide 18 CLK R D S N Let s complete the timing diagram below, then make some notes about D latch behaviour. CLK 1 D 1 S 1 R 1 1

19 SN s ENEL 353 Fall 216 Slide Set 7 slide 19/45 Symbols for D latches and D flip-flops Left: D latch. Right: D flip-flop. CLK CLK D D The symbols look very similar, but there is a really significant difference in behaviour! We ll now move on to studying D flip-flops, which are very important sequential logic elements.

20 SN s ENEL 353 Fall 216 Slide Set 7 slide 2/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

21 SN s ENEL 353 Fall 216 Slide Set 7 slide 21/45 D Flip-Flops: Essential components in almost all sequential circuits!!! In learning about combinational logic circuits, it would be impossible to make progress without knowing exactly what NOT, AND and OR gates do. Similarly, it is impossible to understand most sequential circuits without knowing exactly what the basic behaviour of a D flip-flop is... how the state of a D flip-flop changes in response to its input signals.

22 SN s ENEL 353 Fall 216 Slide Set 7 slide 22/45 Clock edges Transitions between logic levels in a clock signal are usually called clock edges. A 1 transition is called a rising edge or a positive edge. A 1 transition is called a falling edge or a negative edge. Let s make a sketch of a clock signal and label the rising and falling edges.

23 SN s ENEL 353 Fall 216 Slide Set 7 slide 23/45 A good quote from your textbook From page 114 of Harris and Harris: A D flip-flop copies D to on the rising edge of the clock, and remembers its state at all other times. Reread this definition until you have it memorized; one of the most common problems for beginning digital designers is to forget what a flip-flop does.

24 SN s ENEL 353 Fall 216 Slide Set 7 slide 24/45 Learning D flip-flip behaviour by example CLK Let s complete the timing diagram. D CLK 1 D 1 1 1

25 SN s ENEL 353 Fall 216 Slide Set 7 slide 25/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

26 SN s ENEL 353 Fall 216 Slide Set 7 slide 26/45 D flip-flop implementation using two D latches: master-slave configuration D IN CLK input for flip-flop CLK CLK D N1 D OUT Your instructor thinks that grabber-holder would be a more descriptive (and less creepy) name than master-slave for this kind of D flip-flop design. master slave latch latch D flip-flop Let s make some notes on the jobs done by the master and slave latches in this circuit.

27 CLK input for flip-flop slide 27 D IN CLK D N1 CLK D OUT master slave latch latch D flip-flop Let s see how this circuit works by completing this diagram... flip-flop CLK 1 1 D IN 1 N1 1 OUT

28 SN s ENEL 353 Fall 216 Slide Set 7 slide 28/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

29 The clock divider slide 29 This simple and useful circuit can be built with a D flip-flop and an inverter. The output CLK2 is a clock signal with half the frequency of the input CLK1. CLK1 If the frequency of CLK1 is, say, 1 khz, the signals will look like this on an oscilloscope... CLK1 CLK2 D CLK2 The basic behaviour of a D flip-flop explains why CLK2 is constant between rising edges of CLK1. But what is going on at those rising edges? According to the inverter, D =, but according to the flip-flop, = D. It seems like D has to be and 1 at the same time!

30 SN s ENEL 353 Fall 216 Slide Set 7 slide 3/45 How the clock divider works We already know that the inverter has a minimum delay t cd. The flip-flop is a physical device, so also has a minimum delay, which is called t ccq. Let s make some notes about t ccq. CLK1 D CLK2 Now let s study what happens when = just before a rising edge of CLK1, and when = 1 just before a rising edge of CLK1.

31 SN s ENEL 353 Fall 216 Slide Set 7 slide 31/45 A small amount of delay is a good thing! We ve just seen that delays in the clock divider circuit are essential in making it work. The same idea is true for most other systems built using D flip-flops. Of course, long delays are bad they result in circuits that are slow or unreliable, or both. Note: There is much more to learn about timing of flip-flop circuits, but we won t do that until we get to Section 3.5 of Harris & Harris.

32 SN s ENEL 353 Fall 216 Slide Set 7 slide 32/45 About the clock edges visible on the scope... A few slides back it was suggested that if the clock divider input frequency was 1 khz, the input and output signals would look like this on an oscilloscope... CLK1 CLK2 Why do all the clock edges appear to be perfectly vertical? Why do the edges on CLK2 appear to occur at exactly the same time as rising edges on CLK1?

33 SN s ENEL 353 Fall 216 Slide Set 7 slide 33/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

34 SN s ENEL 353 Fall 216 Slide Set 7 slide 34/45 Abbreviations for D flip-flop DFF is short, simple and obvious, so we ll use it in this course. Some literature uses the term flop, which is short but possibly ambiguous.

35 SN s ENEL 353 Fall 216 Slide Set 7 slide 35/45 Symbols for D flip-flops In symbols, the triangle on the CLK input indicates an edge-triggered device. With output... D CLK Lacking output... D CLK D Lacking output, condensed symbol... CLK All DFF designs have an internal signal, but many of them, to save space and power, do not make available as an output.

36 SN s ENEL 353 Fall 216 Slide Set 7 slide 36/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

37 SN s ENEL 353 Fall 216 Slide Set 7 slide 37/45 N-bit registers An N-bit register is a group of N DFFs with a common CLK input. At right, (a) shows 4 DFFs configured as a 4-bit register, and (b) is a symbol for that register. Let s make some notes about the symbol. D 3 D 2 D 1 D (a) D D D D CLK CLK 4 4 D 3: 3: Image is taken from Figure 3.9 from Harris D. M. and Harris S. L., Digital Design and Computer Architecture, 2nd ed., c 213, Elsevier, Inc. (b)

38 SN s ENEL 353 Fall 216 Slide Set 7 slide 38/45 Enabled D flip-flops D EN This kind of DFF is good for a circuit design in which it is useful to have a flip-flop sometimes hold its state for many clock cycles, rather than copy D on every single rising edge of the clock. Let s write a precise description of the behaviour of an enabled DFF. Let s show how an enabled DFF can be built using a plain DFF and a 2:1 multiplexer.

39 SN s ENEL 353 Fall 216 Slide Set 7 slide 39/45 Resettable D flip-flops Here are two symbols for the same thing... D RESET r Let s write a precise description of the behaviour of a resettable DFF, then build one using a plain DFF, an AND gate, and an inverter What would DFFs with reset inputs be useful for?

40 SN s ENEL 353 Fall 216 Slide Set 7 slide 4/45 Variations on enabled and resettable DFFs Here is a pretty obvious variation on the resettable DFF... On each rising edge of CLK, { D if SET = D = 1 if SET = 1 SET s Many textbooks use the names PRESET and CLEAR instead of SET and RESET. Also note that the above is a synchronous SET some DFFs have asynchronous SET and/or RESET. Some DFFs are designed to support two or all three of RESET, SET and EN inputs.

41 SN s ENEL 353 Fall 216 Slide Set 7 slide 41/45 The rest of Section 3.2 in Harris & Harris Section presents and explains the most common present-day transistor-level designs for D latches and DFFs. We will not cover this topic in ENEL 353. If you are curious about this material, you will have to go back and read Section 1.7 before reading Section Section has a good example illustrating the difference between a D latch and a DFF. Check it out carefully!

42 SN s ENEL 353 Fall 216 Slide Set 7 slide 42/45 Outline of Slide Set 7 Combinational versus Sequential Logic SR latches Clock signals The D latch Introduction to D Flip-Flops D flip-flop implementation using two D latches The clock divider Abbreviations and symbols for D flip-flops N-bit registers, enabled DFFs, resettable DDFs Synchronous and asynchronous sequential circuits

43 SN s ENEL 353 Fall 216 Slide Set 7 slide 43/45 Synchronous and asynchronous sequential circuits A synchronous sequential circuit is a sequential logic system that has one or more bits of state; and has its state updates controlled by a clock signal, so that the state updates are synchronized by the clock. Making digital systems synchronous is a very powerful design technique the vast majority of digital circuits, including just about all practical computer processors, are synchronous sequential systems. An asynchronous sequential circuit is a sequential logic system in which some state updates occur not synchronized by the clock.

44 SN s ENEL 353 Fall 216 Slide Set 7 slide 44/45 Synchronous and asynchronous reset of DFFs FF1 has synchronous reset but FF2 has asynchronous reset. Let s complete the timing diagram to show the difference in behaviour. CLK FF1 D r 1 FF2 r R 2 CLK 1 D 1 R

45 SN s ENEL 353 Fall 216 Slide Set 7 slide 45/45 Textbook examples of asynchronous sequential circuits Section in Harris & Harris presents two asynchronous sequential circuits with problematic behaviour: A ring oscillator made from 3 inverters. A D latch design that fails if delays within its components aren t exactly right. In ENEL 353, we re going to move on to synchronous sequential circuits, but it s worth studying these examples to get an idea of the difficulties that can arise in sequential circuits that are not run by a clock signal.

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