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DIGITAL LOGIC DESIGN

DIGITAL LOGIC DESIGN. by Dr. Fenghui Yao Tennessee State University Department of Computer Science Nashville, TN. Note. Most of the figures are from your course book. Sequential Circuits. Combinational The outputs depend only on the current input values It uses only logic gates

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DIGITAL LOGIC DESIGN

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  1. DIGITAL LOGIC DESIGN by Dr. Fenghui Yao Tennessee State University Department of Computer Science Nashville, TN Sequential Circuits

  2. Note • Most of the figures are from your course book Sequential Circuits

  3. Sequential Circuits • 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 • They are referred as finite state machines since they have a finite number of states Sequential Circuits

  4. Block Diagram • Memory elements can store binary information • This information at any given time determines the state of the circuit at that time Sequential Circuits

  5. 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 • If memory elements use clock pulses in their inputs, the circuit is called • Clocked sequential circuit Sequential Circuits

  6. 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 Sequential Circuits

  7. 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 Sequential Circuits

  8. Flip-Flops • They are memory elements • They can store binary information Sequential Circuits

  9. 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 Sequential Circuits

  10. 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 Sequential Circuits

  11. SR Latch with NOR Sequential Circuits

  12. SR Latch with NOR Sequential Circuits

  13. SR Latch with NAND Sequential Circuits

  14. SR Latch with NAND Sequential Circuits

  15. SR Latch with Control Input Sequential Circuits

  16. D Latch Sequential Circuits

  17. Symbols for Latches Sequential Circuits

  18. 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) Sequential Circuits

  19. How to Solve? • Trigger the flip-flop only during a signal transition Sequential Circuits

  20. Edge-Triggered D Flip-Flop Sequential Circuits

  21. Characteristics of D Flip-Flop Sequential Circuits

  22. Edge-Triggered J-K Flip-Flop How??????? Sequential Circuits

  23. Excitation Table Sequential Circuits

  24. Edge-Triggered T Flip-Flop Sequential Circuits

  25. Excitation Table Sequential Circuits

  26. 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 Sequential Circuits

  27. D Flip-Flop with Asynchronous Reset Sequential Circuits

  28. State Equations A state equation shows the next state as a function of the current state and inputs Sequential Circuits

  29. State Table Sequential Circuits

  30. State Diagram Sequential Circuits

  31. Analysis with D Flip-Flops Sequential Circuits

  32. 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 Sequential Circuits

  33. State Reduction Example Find the states for which the next states and outputs are the same Sequential Circuits

  34. Example (Cont.) In the next state, g is replaced with e In the next state, f is replaced with d Sequential Circuits

  35. Example (Cont.) Sequential Circuits

  36. 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 Sequential Circuits

  37. State Assignments Sequential Circuits

  38. 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 Sequential Circuits

  39. Example • Design a circuit (with D flip-flops) that detects three or more consecutive 1’s in a string of bits coming through an input line Sequential Circuits

  40. Example (Cont.) Sequential Circuits

  41. Example (Cont.) Sequential Circuits

  42. Example (Cont.) Sequential Circuits

  43. Example • Design a circuit (with JK flip-flops) that detects three or more consecutive 1’s in a string of bits coming through an input line Sequential Circuits

  44. Example (Cont.) Sequential Circuits

  45. Example (Cont.) Sequential Circuits

  46. Example (Cont.) Sequential Circuits

  47. Study Problems • Course Book Chapter – 5 Problems • 5 – 3 • 5 – 5 • 5 – 6 • 5 – 7 • 5 – 10 • 5 – 12 • 5 – 13 • 5 – 19 Sequential Circuits

  48. Questions Sequential Circuits

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