DIGITAL LOGIC DESIGN

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

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

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

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

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

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

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

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

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

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

SR Latch with NOR Sequential Circuits

SR Latch with NAND Sequential Circuits

SR Latch with Control Input Sequential Circuits

D Latch Sequential Circuits

Symbols for Latches Sequential Circuits

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

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

Edge-Triggered D Flip-Flop Sequential Circuits

Characteristics of D Flip-Flop Sequential Circuits

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

Excitation Table Sequential Circuits

Edge-Triggered T Flip-Flop Sequential Circuits

Excitation Table Sequential Circuits

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

D Flip-Flop with Asynchronous Reset Sequential Circuits

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

State Table Sequential Circuits

State Diagram Sequential Circuits

Analysis with D Flip-Flops Sequential Circuits

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

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

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

Example (Cont.) Sequential Circuits

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

State Assignments Sequential Circuits

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

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

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

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

Questions Sequential Circuits

DIGITAL LOGIC DESIGN