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Sequential Circuits1 DIGITAL LOGIC DESIGN by Dr. Fenghui Yao Tennessee State University Department of Computer Science Nashville, TN Slide 2 Sequential Circuits2 Note Most of the figures are from your course book Slide 3 Sequential Circuits3 Combinational The outputs depend only on the current input values It uses only logic gates Sequential The outputs depend on the current and past input values It uses logic gates and storage elements Example Vending machine Vending machine They are referred as finite state machines since they have a finite number of states Slide 4 Sequential Circuits4 Block Diagram Memory elements can store binary information This information at any given time determines the state of the circuit at that time Slide 5 Sequential Circuits5 Sequential Circuit Types Synchronous The circuit behavior is determined by the signals at discrete instants of time The memory elements are affected only at discrete instants of time A clock is used for synchronization Memory elements are affected only with the arrival of a clock pulse Memory elements are affected only with the arrival of a clock pulse If memory elements use clock pulses in their inputs, the circuit is called If memory elements use clock pulses in their inputs, the circuit is called Clocked sequential circuit Slide 6 Sequential Circuits6 Sequential Circuit Types ASynchronous The circuit behavior is determined by the signals at any instant of time It is also affected by the order the inputs change Slide 7 Sequential Circuits7 Clock It emits a series of pulses with a precise pulse width and precise interval between consecutive pulses Timing interval between the corresponding edges of two consecutive pulses is known as the clock cycle time, or period Slide 8 Sequential Circuits8 Flip-Flops They are memory elements They can store binary information Slide 9 Sequential Circuits9 Flip-Flops Can keep a binary state until an input signal to switch the state is received There are different types of flip-flops depending on the number of inputs and how the inputs affect the binary state Slide 10 Sequential Circuits10 Latches The most basic flip-flops They operate with signal levels The flip-flops are constructed from latches They are not useful for synchronous sequential circuits They are useful for asynchronous sequential circuits Slide 11 Sequential Circuits11 SR Latch with NOR Slide 12 Sequential Circuits12 SR Latch with NOR Slide 13 Sequential Circuits13 SR Latch with NAND Slide 14 Sequential Circuits14 SR Latch with NAND Slide 15 Sequential Circuits15 SR Latch with Control Input Slide 16 Sequential Circuits16 D Latch Slide 17 Sequential Circuits17 Symbols for Latches Slide 18 Sequential Circuits18 Note The control input changes the state of a latch or flip-flop The momentary change is called a trigger Example: D Latch It is triggered every time the pulse goes to the logic level 1 As long as the pulse remains at the logic level 1, the change in the data (D) directly affects the output (Q) THIS MAY BE A BIG PROBLEM since the state of the latch may keep changing depending on the input (may be coming from a combinational logic network) Slide 19 Sequential Circuits19 How to Solve? Trigger the flip-flop only during a signal transition Slide 20 Sequential Circuits20 Edge-Triggered D Flip-Flop Slide 21 Sequential Circuits21 Characteristics of D Flip- Flop Slide 22 Sequential Circuits22 Edge-Triggered J-K Flip-Flop How??????? Slide 23 Sequential Circuits23 Excitation Table Slide 24 Sequential Circuits24 Edge-Triggered T Flip-Flop Slide 25 Sequential Circuits25 Excitation Table Slide 26 Sequential Circuits26 Direct Inputs You can use asynchronous inputs to put a flip-flop to a specific state regardless of the clock You can clear the content of a flip-flop The content is changed to zero (0) This is called clear or direct reset This is particularly useful when the power is off The state of the flip-flop is set to unknown The state of the flip-flop is set to unknown Slide 27 Sequential Circuits27 D Flip-Flop with Asynchronous Reset Slide 28 Sequential Circuits28 State Equations A state equation shows the next state as a function of the current state and inputs Slide 29 Sequential Circuits29 State Table Slide 30 Sequential Circuits30 State Diagram Slide 31 Sequential Circuits31 Analysis with D Flip-Flops Slide 32 Sequential Circuits32 State Reduction Reduce the number of states but keep the input-output requirements Reducing the number of states may reduce the number of flip-flops If there are n flip-flops, there are 2^n states If you have two circuits that produce the same output sequence for any given input sequence, the two circuits are equivalent They may replace each other Slide 33 Sequential Circuits33 State Reduction Example Find the states for which the next states and outputs are the same Slide 34 Sequential Circuits34 Example (Cont.) In the next state, g is replaced with e In the next state, f is replaced with d Slide 35 Sequential Circuits35 Example (Cont.) Slide 36 Sequential Circuits36 State Assignment You need to assign binary values for each state so that they can be implemented You need to use enough number of bits to cover all the states Slide 37 Sequential Circuits37 State Assignments Slide 38 Sequential Circuits38 Design Procedure Derive a state diagram Reduce the number of states Assign binary values to the states Obtain binary coded state table Choose the type of flip-flop to be used Derive simplified flip-flop input equations and output equations Draw the logic diagram Slide 39 Sequential Circuits39 Example Design a circuit (with D flip-flops) that detects three or more consecutive 1s in a string of bits coming through an input line Slide 40 Sequential Circuits40 Example (Cont.) Slide 41 Sequential Circuits41 Example (Cont.) Slide 42 Sequential Circuits42 Example (Cont.) Slide 43 Sequential Circuits43 Example Design a circuit (with JK flip-flops) that detects three or more consecutive 1s in a string of bits coming through an input line Slide 44 Sequential Circuits44 Example (Cont.) Slide 45 Sequential Circuits45 Example (Cont.) Slide 46 Sequential Circuits46 Example (Cont.) Slide 47 Sequential Circuits47 Study Problems Course Book Chapter 5 Problems 5 3 5 5 5 6 5 7 5 10 5 12 5 13 5 19 Slide 48 Sequential Circuits48 Questions