Sequential Logic. E&CE 223 Digital Circuits and Systems (A. Kennings) Page 1
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1 Sequential Logic E&CE 223 igital Circuits and Systems (A. Kennings) Page 1
2 Sequential Circuits Have considered only combinational circuits in which circuit outputs are determined entirely by current circuit inputs. We can include storage elements into a circuit that act like memory and store a system state. inputs combinatorial circuit outputs memory elements state Outputs are then a function of both the current circuit inputs and the system state. E&CE 223 igital Circuits and Systems (A. Kennings) Page 2
3 Types of Sequential Circuits Two main types of sequential circuits (classification depends on how timing happens): Synchronous Sequential Circuits circuit behavior is determined from the knowledge of signal values at discrete instances in time. Asynchronous Sequential Circuits - circuit behavior is determined by signals at any instant in time and the order in which input signals change. E&CE 223 igital Circuits and Systems (A. Kennings) Page 3
4 Synchronous Sequential Circuits To control the behavior of a circuit at discrete instances in time, we will need to introduce the concept of a clock. It s a periodic signal consisting of a sequence of pulses. It is used to control the times at which the storage elements in the circuit change their values. The storage elements used can be latches or flip-flops. inputs combinatorial circuit outputs storage elements state clock/ control clock/ control The clock/control connects to the storage elements which are latches or flip-flops. E&CE 223 igital Circuits and Systems (A. Kennings) Page 4
5 Clocks Clocks are periodic. They can control when things happen because their transition from 0! 1 and from 1! 0 occur at discrete instances in time. The 0! 1 transition is often called the rising edge of the clock. The 1! 0 transition is often called the falling edge of the clock. clock 1 0 rising edge (0->1 transition) falling edge (1->0 transition) E&CE 223 igital Circuits and Systems (A. Kennings) Page 5
6 Latches Latches are level sensitive storage elements; They operate based on whether signals are at logic levels 0 or 1, not on logic transitions from 0! 1 or 1! 0. Latches are not really too useful for synchronous sequential circuits (they are for asynchronous circuits), but form the basis from which flip-flops are built. E&CE 223 igital Circuits and Systems (A. Kennings) Page 6
7 SR Latch (NOR Implementation) Illustrated Consider the operation of the following circuit: R (reset) S (set)! E&CE 223 igital Circuits and Systems (A. Kennings) Page 7
8 SR Latch (NOR Implementation) Explained In general (one exception, see below), the outputs are complements of each other (this is why they are labeled and :): When S=1, R=0 the output is =1, :=0 and the circuit in the set state. When S=0, R=1 the output is =0, :=1 and the circuit in the reset state. So, S=1 (active high) implies set (=1) and R=1 (active high) implies reset (=0). When S=0, R=0 the output holds at its previous value (storage). When S=1, R=1 the output is =:=0 which is not desirable. We want to avoid this combination of inputs. E&CE 223 igital Circuits and Systems (A. Kennings) Page 8
9 S R Latch (NAN Implementation) Illustrated Consider the operation of the following circuit: S (set) R (reset)! E&CE 223 igital Circuits and Systems (A. Kennings) Page 9
10 S R Latch (NAN Implementation) Explained In general (one exception, see below), the outputs are complements of each other (this is why they are labeled and :): When S=0, R=1 the output is =1, :=0 and the circuit in the set state. When S=1, R=0 the output is =0, :=1 and the circuit in the reset state. So, S=0 (active low) implies set (=1) and R=0 (active low) implies reset (=0). When S=1, R=1 the output holds at its previous value (storage). When S=0, R=0 the output is =:=1 which is not desirable. We want to avoid this combination of inputs. So, it works similar to the NOR implementation, but the input values are reversed for each of the different cases. E&CE 223 igital Circuits and Systems (A. Kennings) Page 10
11 Latch With Control Input (i.e., Gated Latch) We can add an additional control input that acts as an enable signal. Consider adding some extra NAN gates in front of an S R Latch. This gives us a SR Latch with control input. S C R! E&CE 223 igital Circuits and Systems (A. Kennings) Page 11
12 Latch With Control Input Explained S C R! When the control input C=0, The inputs to the latch are both 1 which puts the SR latch into hold state. The latch outputs will not change regardless of S and R values. E&CE 223 igital Circuits and Systems (A. Kennings) Page 12
13 Latch With Control Input (NAN Implementation) S C R! When the control input C=1, The S and R inputs will reach the latch and we can analyze the behavior. The NAN gates at the input to the latchresult in active high inputs: S=1 (and R=0) causes a set (=1). R=1 (and S=0) causes a reset (=0). E&CE 223 igital Circuits and Systems (A. Kennings) Page 13
14 Latch We must avoid the undesirable situation in which we cannot determine what the output of the latch will be i.e., we never want S=1, R=1 when C=1 (bad!) The solution is to construct a latch where S and R can never have the same value. E&CE 223 igital Circuits and Systems (A. Kennings) Page 14
15 Latch Illustrated C! We still have a hold state when the control input C=0. The output follows input when the control input C=1. E&CE 223 igital Circuits and Systems (A. Kennings) Page 15
16 Schematic Symbol for SR Latch (With and Without Control Input) S S C R R Note: as illustrated, this means the inputs are active high; i.e., we set when S=1 (and R=0) and we reset with R=1 (and S=0). E&CE 223 igital Circuits and Systems (A. Kennings) Page 16
17 Schematic Symbol for S R Latch (With and Without Control Input) S S C R R Note: as illustrated, this means the inputs are active low; i.e., we set when S=0 (and R=1) and we reset with R=0 (and S=1). E&CE 223 igital Circuits and Systems (A. Kennings) Page 17
18 Schematic Symbol for Latch (With Control Input) C Note: For a Latch, the control input is required, since it is via the control input that we have the hold state. E&CE 223 igital Circuits and Systems (A. Kennings) Page 18
19 Textbook Sections Information on Sequential Circuits, Synchronous Sequential Circuits and Latches can be found in the course textbook in Chapter 5, Sections 5.1 and 5.2. E&CE 223 igital Circuits and Systems (A. Kennings) Page 19
20 Problem With Latches Latches do not allow for precise control because they are level sensitive. Consider a -Latch with the clock signal connected to the control input. Output of the latch can change anytime while the clock is at its active level. This creates an interval in time over which the state, or output, of the memory element can change rather that an instant in time at which the state, or output, of the memory element can change. It would be better to only allow the output to change when the clock edge makes a transition from 0! 1 (rising edge triggering) or 1! 0 (falling edge triggering). This gives even more precise control! Flip-flops give more precise control by being edge-triggered. E&CE 223 igital Circuits and Systems (A. Kennings) Page 20
21 Triggering Illustrated Response to positive level (a latch) large window of time for output to change. Positive Edge Triggering. The input to the flip-flop just before the clock changes from 0! 1 causes the output to change just after the clock changes from 0! 1. Negative Edge Triggering. The input to the flip-flop just before the clock changes from 1! 0 causes the output to change just after the clock changes from 1! 0. E&CE 223 igital Circuits and Systems (A. Kennings) Page 21
22 Negative Edge Triggered Flip-Flop (Master-Slave) We can make a negative edge triggered -type flip-flop (FF) using two latches. We connect the clock input to the control input of the first latch (master), and the inversion of the clock input to the control input of the second latch (slave). Latch (master) Y Latch (slave) CLOCK C C E&CE 223 igital Circuits and Systems (A. Kennings) Page 22
23 Operation of Negative Edge Triggered Flip-Flop (Master-Slave) Latch (master) Y Latch (slave) CLOCK C C While CLK=1, Y will follow input via the master latch, but will not follow Y (it is in hold state) and will hold its current value. When CLK=0 (at the moment of change), Y will be disconnected from and will hold its current value. will follow Y via the master latch. The effect is that the value of just prior to the falling edge of the clock will get transferred to the output just after the falling edge of the clock. E&CE 223 igital Circuits and Systems (A. Kennings) Page 23
24 Positive Edge Triggered Flip-Flop (Master-Slave) We can make a positive edge triggered FF simply by changing the inversion of the clock signal Output of master latch, Y, follows when clock is low (slave in hold). Output of slave latch,, follows Y when clock is high (master in hold). Latch (master) Y Latch (slave) CLOCK C C E&CE 223 igital Circuits and Systems (A. Kennings) Page 24
25 Schematic Symbols for FFs We can introduce schematic symbols for FFs. Note the indication of the clock input and the change to the symbols (vs. a latch) to indicate edge-triggering. Positive Edge-Triggered FF: Negative Edge-Triggered FF: E&CE 223 igital Circuits and Systems (A. Kennings) Page 25
26 More Efficient esign of a FF Master-Slave is not the most efficient way to build an edge-triggered FF. The circuit below acts as a positive edge-triggered FF: S CLK R! E&CE 223 igital Circuits and Systems (A. Kennings) Page 26
27 More Efficient esign of a FF Explained (CLK=0) When CLK=0, both S=1 and R=1 and the output latch will hold its state. S 1 hold 0 CLK R 1! E&CE 223 igital Circuits and Systems (A. Kennings) Page 27
28 More Efficient esign of a FF Explained (=0 when CLK=0! 1) When =0 and CLK = 0! 1, R = 1! 0 and the output latch goes into its reset state (=0). Further changes in while CLK=1 cannot change R and = just after clock changes. S 1 reset ->0 0->1 CLK 1->0 R! 0 1 E&CE 223 igital Circuits and Systems (A. Kennings) Page 28
29 More Efficient esign of a FF Explained (=1 when CLK=0! 1) When =1 and CLK = 0! 1, S = 1! 0 and the output latch goes into its set state (=1). Further changes in while CLK=1 cannot change S and = just after clock changes. 0->1 CLK 1 1->0 S 1 R set! ->1 1 0 E&CE 223 igital Circuits and Systems (A. Kennings) Page 29
30 Sets and Resets Sometimes flip-flops will have additional, asynchronous control inputs that force the output to a particular value. An asynchronous signal that forces =1 is called an asynchronous set or preset. The output will remain 1 as long as the set input is active (changes in and CLK are ignored). An asynchronous signal that forces =0 is called an asynchronous clear or reset. The output will remain 0 as long as the reset input is active (changes in and CLK are ignored). E&CE 223 igital Circuits and Systems (A. Kennings) Page 30
31 Reset Illustrated The following circuit has an (active low) asynchronous reset. S 1 reset/ hold 0 CLK RESET 0 0/1 1 R! 1 E&CE 223 igital Circuits and Systems (A. Kennings) Page 31
32 Schematic Symbols for SRFFs (FF With Resets and Sets) Active low set and reset signals. S R Active high set and reset signals. S R E&CE 223 igital Circuits and Systems (A. Kennings) Page 32
33 Characteristic Tables and Equations We can describe the behavior of a flip-flop via a characteristic table. The characteristic table shows what the next flip-flop output value will be given the current flip-flop input value after the clock makes its active edge transition. The characteristic table for a FF is: We can also write this as a characteristic equation: For a FF, the output value becomes the input value when the clock makes its active edge transition. E&CE 223 igital Circuits and Systems (A. Kennings) Page 33
34 Toggle Flip-Flops (TFF) Another type of flip-flop that has a different behavior when compared to a FF. Symbol for a positive edge-triggered TFF: T Symbol for a negative edge-triggered TFF: T E&CE 223 igital Circuits and Systems (A. Kennings) Page 34
35 Behavior of a TFF The characteristic table for the TFF: The characteristic equation for the TFF: So with a TFF, the output toggles (or flips) its value if the input is T=1, otherwise it remains the same. E&CE 223 igital Circuits and Systems (A. Kennings) Page 35
36 Construction Of A TFF Using a FF We can actually build a TFF using a FF and a 2-input XOR gate. T T CLOCK E&CE 223 igital Circuits and Systems (A. Kennings) Page 36
37 JK Flip-Flops (JKFF) Again, another type of flip-flop that has different behavior compared to a FF or to a TFF. Positive edge-triggered JKFF: J K Negative edge-triggered JKFF: J K E&CE 223 igital Circuits and Systems (A. Kennings) Page 37
38 Behavior of a JKFF The characteristic table for the JKFF: We can derive the characteristic equation for the JKFF (I find it easy to explain via a K-Map): JK (t) E&CE 223 igital Circuits and Systems (A. Kennings) Page 38
39 Construction Of A JKFF Using a FF We can actually build a JKFF using a FF and some other gates. J J K CLOCK K E&CE 223 igital Circuits and Systems (A. Kennings) Page 39
40 Circuit Timing With Flip-Flops There are some important things to understand when we go to actually make and implement a circuit with flip-flops. In reality, it takes time for gates to change their output values according to the input values i.e., there are propagation delays due to resistance, capacitance, etc. Changes in flip-flop outputs occur at the active clock edge. There are three timing parameters that are especially important: Setup Time (TSU). Hold Time (TH). Clock-To-Output Time (TCO). E&CE 223 igital Circuits and Systems (A. Kennings) Page 40
41 efinitions Setup Time (TSU): The setup time of a flip-flop is the amount of time that the data inputs need to be held stable (not changing) PRIOR to the arrival of the active clock edge. Hold Time (TH): The hold time of a flip-flop is the amount of time that the data inputs need to be held stable (not changing) AFTER the arrival of the active clock edge. Clock-To-Output (TCO): The clock-to-output time of a flip-flop is the amount of time it takes for the output to become stable (at its new value) AFTER the arrival of the active clock edge. E&CE 223 igital Circuits and Systems (A. Kennings) Page 41
42 Comments If these timing specifications are not met, then it is possible that the flip-flop will not behave as expected. That is, if we don t observe setup and hold times at the data inputs, then our output might not change as expected. That is, if we don t wait long enough (clock-to-output time) for the output to change, then we might use an incorrect value. If we violate any of these timing parameters, then we have a timing violation. These timing parameters (as we will see later) have an influence on how fast we can clock a circuit. E&CE 223 igital Circuits and Systems (A. Kennings) Page 42
43 Timing Parameters Illustrated (Using A FF) TSU TH TCO CLOCK should not change in this interval not stable (trustworthy) until this interval ends E&CE 223 igital Circuits and Systems (A. Kennings) Page 43
44 Textbook Sections Information on Flip-Flops can be found in the course textbook in Chapter 5, Section 5.3. E&CE 223 igital Circuits and Systems (A. Kennings) Page 44
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