# So far we have investigated combinational logic for which the output of the logic devices/circuits depends only on the present state of the inputs.

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1 equential Logic o far we have investigated combinational logic for which the output of the logic devices/circuits depends only on the present state of the inputs. In sequential logic the output of the logic device is dependent not only on the present inputs to the device, but also on past inputs; i.e., the output of a sequential logic device depends on its present internal state and the present inputs. This implies that a sequential logic device has some kind of memory of at least part of its history (i.e., its previous inputs). equential logic devices have some sort of feedback, where the output of some logic device is fed back to the input of a logic device. A simple memory circuit constructed from a O gate is shown on Figure. A Figure. In this memory device, if A and are initially at logic, then remains at logic. However if A becomes a logic, then the output will be logic ever after, regardless of any further changes in the input at A. Once = has been written it can t be changed back but it can be read. You may also think of this as a one time programmable memory element. Not a very useful circuit arrangement but it gave us our first exposure to positive feedback and memory. Let s now consider a circuit consisting of two inverters connected in a loop as shown on Figure 2. Vi A Vi A B Vo B Vo Figure 2. Fundamental latch The voltage transfer characteristic of this circuit is shown on Figure 3. Note that the circuit has two stable states and it is thus called bistable circuit. This pair of inverters is also called a latch. 6.7/22.7 pring 26, Chaniotakis and Cory

2 Vo Voltage transfer curve 3 Vo=Vi load line stable -point 2 unstable -point stable -point Vi A B Vo Figure 3. Voltage transfer characteristic of a latch (bistable circuit) The operating points (-points) for this circuit must lie on the voltage transfer curve. Furthermore the loop connection imposes that the input and output voltages must be the same. Therefore the load line of this circuit is a line of slope as indicated on Figure 3. The operating points must also lie on the load line curve. Therefore the only possible operating points are those defined by the interception of the voltage transfer characteristic curve and the load line. These points are denoted by, 2 and 3 on Figure 3. Of these 3 possible operating points only 2, and 3, are stable and therefore realizable. Point 2 is unstable. Indeed if we assume that the circuit is operating at 2 then due to the positive feedback characteristic of the system, any small deviation in the input, whether positive or negative, will drive the output to the top operating point 3 or to the bottom operating point respectively. The fundamental principles of sequential logic show us how to construct circuits that switch from one operating point to the other. Vi The et-eset () Flip-Flop. The flip-flop is shown on Figure 4. G G Figure 4. Flip-Flop. Circuit and symbol 6.7/22.7 pring 26, Chaniotakis and Cory 2

3 This sequential logic circuit is constructed with NO gates and it has inputs labeled and which may assume the values or. An equivalent representation of the circuit is shown on Figure 5 where the feedback loop is clearly shown. G G Figure 5. Flip-Flop The outputs and are complementary. The function of the circuit is described by the table n n- Not allowed This table, called the function table, represents the dynamics of the system, not just the static logic described in combinational logic circuits and represented by the truth table. n represents the current state of the output and n- corresponds to the previous state. In order to understand the behavior of the circuit let s first consider the following scenaria.. =, =. In this case the output of NO gate G must be ( = ). Now both inputs of gate G are and so the output of G must be. o = and =. In this case we say that the flip-flop is ET 2. =, =. In this case the output of NO gate G must be ( = ). Now both inputs of gate G are and so the output of G must be. o = and =. In this case we say that the flip-flop is EET. Note that the notation make sense. When changed from to the output was EET. 3. =, =. In this case the output can be either or. In fact the output in this case depends on its previous value. To see this explicitly consider the sequence of events. 6.7/22.7 pring 26, Chaniotakis and Cory 3

4 n =, n = n =, n = G G n+ =, n+ = n+ =, n+ = G Note that if goes back to the state of the output does not change. For the output to change state, the state of must change. In this case the flipflop will be ET G G G 4. =, =. Not Allowed. In this case both outputs will try to go to. It is impossible to predict which output will go to and which will stay at. The dynamic characteristics of the flip-flop can be explicitly represented by the timing diagram shown below. The diagram on the left shows the transitions without any time delay. On the right the incorporation of time delay, td, through each gate is indicated in an exaggerated way for the purpose of the demonstration. td td td td time The flip-flop may also be constructed with NAND gates as shown on Figure 6. time G G Figure 6. NAND implementation of flip-flop 6.7/22.7 pring 26, Chaniotakis and Cory 4

5 Clocked Flip-Flop Flip-Flops become very useful devices once we control their operation with some type of control signal. For example we might be interested in capturing data that is available for a short amount of time or at regular intervals. When a clock pulse is used as the control signal the inputs and may be clocked (entered) into the flip-flop by a set of AND gates as shown on Figure 7. ' G ' G Figure 7. Clocked Flip-Flop and its symbol. The obvious advantage of this clocked flip-flop is that the inputs and are considered only when the clock pulse is high. As before the condition = = is indeterminate and should be avoided. A typical timing diagram for the clocked flip flop is shown on Figure 8. not clocked time Figure 8. Timing diagram of clocked flip-flop 6.7/22.7 pring 26, Chaniotakis and Cory 5

6 Note that the output responds to the clock pulse. The dashed line labeled not clocked represents the output of the non-clocked flip-flop. For a finer control of the flip we may, with the circuit modification shown on Figure 9, enable signals and during the raising edge of the clock pulse. The delay is introduced by the inverter and the clocking is accomplished during the delay time. ' G ' G Figure 9. Positive (raising) edge triggered flip-flop and related symbol imilarly the triggering, i.e enabling of the and signals may be accomplished during the falling edge with the circuit implementation shown on Figure. ' G o ' G Figure. Negative (falling) edge triggered flip-flop and related symbol A variation of the standard flip-flop is the Master-lave flip-flop. The corresponding circuit schematic is Master lave ' A G G ' G A G This flip-flop is made up of two flip-flops connected in series. The clock pulse to the second flip-flop (the lave) is inverted. A the positive clock transition the output of the Master gets ET but without affecting the lave. The lave is in turn triggered during the negative (falling) clock pulse transition. 6.7/22.7 pring 26, Chaniotakis and Cory 6

7 JK Flip-Flop The fundamental disadvantage of the flip-flop is the indeterminate state of the output when the inputs and simultaneously assume the state of. A modification of the flip-flop, called the JK flip flop removes this problem. The schematic of the JK flip-flop is shown on Figure. J J K K Figure. JK flip-flop and its symbol. The fundamental difference of this device is the feedback paths to the AND gates of the input. The function table for this very useful device is J K n n- n- 6.7/22.7 pring 26, Chaniotakis and Cory 7

8 For enhanced functionality the JK flip-flop is designed with a PEET and a CLEA pin. The schematic and the functional table for this JK flip-flop is shown below. PE J O O K O CL PE CL J K n n X X X X X X X X X Not used n- n- n- n- X X n- n- toggle Note that the PEET and CLEA override J, K and completely. o if PEET goes to, then goes to ; and if CLEA goes to, then goes to no matter what J, K and are doing. If both PEET and CLEA are, then J, K and can contribute as we have learned above for a JK flip-flop. o at the falling edge the J and K inputs are stored ( n = J and = K) if J and K are opposites. n If both J and K are at the low-going edge, then the outputs toggle. 6.7/22.7 pring 26, Chaniotakis and Cory 8

9 The T Flip-Flop The T (trigger) flip-flop is a one input flip-flop which may be constructed by simply connecting the inputs of the JK flip-flop together as shown on Figure 2. Equivalently the T flip-flop may be constructed by connecting and setting to the inputs of the JK flip-flop. In this case the output simply toggles after each pulse. T T Figure 2. T flip-flop and related symbol. The function table of the T flip-flop is T n n- n- With the JK inputs connected to as shown below the output of the flip-flop results in a signal with half the clock frequency J K time 6.7/22.7 pring 26, Chaniotakis and Cory 9

10 In the following circuit three JK flip flops (in a T configuration) are arranged as indicated. Draw the resulting outputs, and 2 +5V J K J J K K /22.7 pring 26, Chaniotakis and Cory

11 The D Flip-Flop The D (Delay or Data) flip-flop is a one input flip-flop which may be constructed from the standard flip-flop as shown on Figure 3. D Figure 3. D Flip-Flop The function table for the D flip-flop is shown below. Note that the conditions == and == can not exist in this configuration. A clocked D flip-flop is shown on Figure 4. D n n ET EET D ' G D ' G Figure 4. Clocked D flip-flop The functional characteristics of the clocked D flip-flop are: D n ET EET 6.7/22.7 pring 26, Chaniotakis and Cory

12 A typical timing diagram of the clocked D flip-flop is shown on Figure 4. The dotted vertical lines are the times at which transitions occur D time Figure 4. Timing diagram of D Flip-Flop 6.7/22.7 pring 26, Chaniotakis and Cory 2

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