DESIGN OF SEQUENTIAL CIRCUITS by Dr. Amin Danial Asham

References  Digital Design 5 th Edition, Morris Mano

 State Reduction (continue)  In sequential circuits the input and output sequences are important and the internal state role is just to produce these sequences.  As an example, a sequential circuit with the following state diagram: o The states are denoted by letter since the binary values are not important. o Using the state diagram we get the output sequence corresponding to the input sequence

 State Reduction (continue)  If input-output is considered, two sequential circuits with different number of FF’s are considered equivalent if each input sequence applied to the two circuits produces the same output sequence.  “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.”  If there are two equivalent states, one of them can be removed without changing the input-output relations.  Now to reduce the number of states, the state table will be used and searching for equivalent states.

 State Reduction (continue)

 Replacing the removed state with its equivalent in the table.

 State Reduction (continue)  Replacing the removed state with its equivalent in the table.

3 FF’s 5 FF’s

 State Assignment (continue)  The reduced 5 states in our example are coded using binary code.  Three bits can be used to code 8 states, we used 5 states and the other 3 states are considered don’t care.  The state table using the binary assignment is sometimes called the transition table to be distinguished from the state table with symbolic names for the states.

 Design Procedure 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 binary-coded state table. 5.Choose the type of flip-flops to be used. 6.Derive the simplified flip-flop input equations and output equations. 7.Draw the logic diagram.

 Example  Design a circuit that detects a sequence of three or more consecutive 1’s in an input stream.  The state diagram of this detector can be as shown. o There are four states S 0, S 1, S 2, and S 3, which represents 0 at input, single 1, two consecutive 1’s, or three or more consecutive 1’s respectively. o The output of this detector is 1 when 3 or more consecutive 1’s are detected.

Input Equations

 Example – D FF implementation (continue)  Since the input and output equations are written down as sum of minterms, therefore the these equation can be simplified using K-maps.

 Example – D FF implementation (continue)

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