Digital Design, Kyung Hee Univ. Chapter 5. Synchronous Sequential Logic


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1 Chapter 5. Synchronous Sequential Logic 1
2 5.1 Introduction Electronic products: ability to send, receive, store, retrieve, and process information in binary format Dependence on past values of inputs Sequential circuit act as storage elements and have memory FIGURE 5.1 Block diagram of sequential circuit 2
3 5.2 Sequential Circuits Output: a function of inputs and the present state of the storage elements Next state of the storage elements: a function of external inputs and the present state A sequential circuit is specified by a time sequence of inputs, outputs, and internal states vs. Combinational circuit depends on the present values of the inputs Classification (timing of signals) Asynchronous sequential circuit: at any instant of time and order Timedelay devices Internal propagation delay of logic gate Combinational circuit with feedback Unstable at times Synchronous sequential circuit= clocked sequential circuit: at discrete instants of time 3
4 Synchronous Sequential Circuit Signals affect the storage elements at only discrete instants of time Synchronization (by a timing device = clock generator, periodic train of clock pulses: Clock, Clk) Flipflop Storage elements used in clocked sequential circuits Capable of storing one bit of information FIGURE 5.2 Synchronous clocked sequential circuit 4 Considering propagation delay Occurring transition only at predetermined intervals dictated by the clock pulses
5 5.3 Storage elements: Latches Maintain a binary state indefinitely until directed by an input signal to switch states Various types of storage elements: number of inputs, manner affecting the binary state Level sensitive devices: Latch (operate with signal levels) For asynchronous sequential circuits Edgesensitive devices: Flipflops (controlled by a clock transition) For synchronous sequential circuits 5
6 SR Latch A circuit with two crosscoupled NOR gates or two crosscoupled NAND gates Two inputs: S for set and R for reset 00 : remain, latch 11 : unpredictable / undefined state / metastable state FIGURE 5.3 SR latch with NOR gates 6
7 S R Latch FIGURE 5.4 SR latch with NAND gates FIGURE 5.5 SR latch with control input 7
8 D Latch (Transparent Latch) To eliminate the undesirable condition of the indeterminate state in SR latch FIGURE 5.6 D latch FIGURE 5.7 Graphic symbols for latches 8
9 5.4 Storage Elements: FlipFlops Switched the state of a latch or flipflop by a change in the control input Momentary change = trigger the flipflop Employ a common clock Trigger it only during a signal transition Positive edge / negative edge Flipflop Employ two latches Trigger only during a signal transition of the synchronizing signal FIGURE 5.8 Clock response in latch and flipflop 9
10 EdgeTriggered D FlipFlop Two D latches and an inverter Sampling D input and changing its output at the negative edge of the synchronizing or controlling clock Output value stored in the master stage immediately before the negative edge occurred (1) the output may change only once (2) a change in the output is triggered by the negative edge of the clock (3) the change may occur only during the clock s negative level FIGURE 5.9 Master slave D flipflop 10
11 EdgeTriggered D Flipflop Used three SR latches When Clk=0, S=R=1 (no change) When Clk changes from 0 to 1, If D=0, R=0 (Reset state) If D=1, S=0 (Set state) T2 FIGURE 5.10 Dtype positiveedgetriggered flipflop Clk D X 0 1 X 1 0 T T S R Q T1 11
12 Setup time: minimum time of D input maintained at a constant value prior to the occurrence of the clock transition Hold time: minimum time of D input maintained at a constant value after the clock transition Propagation delay time: interval between the trigger edge and the stabilization of the output to a new state Dynamic indicator(>) Edgetriggered D flipflop: the most economical and efficient FIGURE 5.11 Graphic symbol for edgetriggered D flipflop 12
13 JK FlipFlop Operations Set as 1 (J=1, K=0) Reset as 0 (J=0, K=1) Complement its output (J=K=1) Unchanged (J=K=0) Q(t+1)=JQ +K Q 13 FIGURE 5.12 JK flipflop
14 T FlipFlop D=TQ +T Q FIGURE 5.13 T flipflop Q(t+1)=D Q(t+1)=TQ +T Q 14
15 Characteristic Tables / Equations Characteristic table Logical properties of a flipflop by describing its operation in tabular form A function of the inputs and the present state Characteristic equation Express algebraically D F/F: Q(t+1)=D JK F/F: Q(t+1)=JQ +K Q T F/F: Q(t+1)=TQ +T Q Direct Inputs Asynchronous inputs to force the flipflop to a particular state independently of the clock Preset/Direct set: set F/F as 1 Clear/Direct reset: clear F/F as 0 Set all flipflops in the system to a known starting state prior to the clocked operation 15
16 FIGURE 5.14 D flipflop with asynchronous reset
17 5.5 Analysis of Clocked Sequential Circuits Analysis: behavior of a given circuit under certain operating conditions Clocked sequential circuit including flipflops is determined from the inputs, the outputs, and the internal state of its F/F Representation Algebraic representation State table State diagram Time sequence of inputs, outputs, and internal states 17
18 State Equations (Transition Equation) The next state as a function of the present state and inputs D F/F: Q(t+1)=D A(t+1)=A(t)x(t)+B(t)x(t) B(t+1)=A (t)x(t) y(t)=[a(t)+b(t)]x (t) Zerodetector FIGURE 5.15 Example of sequential circuit 18
19 State Table Enumerate time sequence of inputs, outputs, and internal F/F states in a state table (a transition table) A(t+1)=Ax+Bx B(t+1)=A x y=ax +Bx m flipflops n inputs 2^(m+n) rows in the state table Next states: m columns for each 19
20 State Diagram State: circle Transitions between states (directed lines) State of F/F (binary number in the circle) Input/output Circuit diagram Equations State table State diagram 0/0 1/0 0/ /1 1/0 0/1 1/ /0
21 FlipFlop Input Equations 21
22 Analysis with DF/F State equation = input equation FIGURE 5.17 with D flipflop Sequential circuit 22
23 1.Determine the flipflop input equations in terms of the present state and input variables 2.List the binary values of each input equation 3.Use the corresponding flipflop characteristic table to determine the next state values in the state table FIGURE 5.18 Sequential circuit with JK flipflop 23
24 24
25 Input equation 1. Determine the flipflop input equations in terms of the present state and input variables 2. Substitute the input equations into the flipflop characteristic equation to obtain the state equations 3. Use the corresponding state equation to determine the next state values in the state table Q(t+1)=JQ +K Q Characteristic equation State equation FIGURE 5.19 of Fig State diagram of the circuit 25
26 26
27 Analysis with T F/F Characteristic equation Output equation State equation Input equation FIGURE 5.20 Sequential circuit with T flipflops (Binary Counter) 27
28 Mealy and Moore Models of FSM Moore model: outputs are synchronized with clock Mealy model: value presented immediately before the active edge of the clock FIGURE 5.21 Block diagrams of Mealy and Moore state machines 28
29 5.7 State Reduction and Assignment Analysis: a circuit diagram state table or diagram Design(synthesis): a set of specifications logic diagram Simplify a design by reducing the number of gates and F/Fs State reduction To find ways of reducing the number of states in a sequential circuit without altering the inputoutput relationships Important only inputoutput sequences State a a b c d e f f g f g a Input output
30 State Reduction Two states are said to be equivalent if, for each member of the set of inputs, they give exactly the same output and send the circuit either to the same state or to an equivalent state 30
31 State a a b c d e f f g f g a Input output
32 State Assignment Transition table 32
33 5.8 Design Procedure Manal design method using D, JK, and T F/F Start from a set of specifications and culminate in a logic diagram (or list of Boolean functions) 1 st step: obtain a state table or a state diagram Synchronous sequential circuit = F/F + combinational gates 1. From the word description and specifications of the desired operation, derive a state diagram for the circuit 2. Reduce the number of states if necessary 3. Assign binary values to the states 4. Obtain the binarycoded state table 5. Choose the type of flipflops to be used 6. Derive the simplified flipflop input equations and output equations 7. Draw the logic diagram Steps 4~7: welldefined procedure=synthesis 33
34 Example: How obtained a state diagram Detect a sequence of three or more consecutive 1 s in a string of bits coming through an input line FIGURE 5.27 State diagram for sequence detector 34
35 Synthesis using D F/F Need to assign binary codes to the states and list the state table Choose two D F/F to represent the four states 35
36 FIGURE 5.29 Logic diagram of a Mooretype sequence detector 36
37 Excitation Tables Necessary to derive a functional relationship between the state table and the input equations (JK and T F/F) Excitation table: list the required inputs for a given change of state 37
38 Synthesis using JK F/F Input equations derived from the excitation table FIGURE 5.30 Maps for J and K input equations 38
39 FIGURE 5.31 Logic diagram for sequential circuit with JK flipflops 39
40 Synthesis using T F/F Binary counter (0 to 2 n 1) 40
41 FIGURE 5.34 Logic diagram of threebit binary counter 41
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