Analysis of Fundamental Mode Sequential Circuits

Analysis of Fundamental Mode Sequential Circuits

AU : Dec.-10, 11, 12, Hay-12, 13

• Fundamental mode asynchronous sequential circuit analysis requires careful attention because these circuits utilize unclocked memory and level inputs. The procedure to analyze these circuits is as follows :

1. Determine the next-secondary state and output equations from given sequential circuit.

2. Construct the state table.

3. Construct the transition table.

4. Construct output map.

Examples for Understanding

Ex. 7.5.1 Analyze the fundamental mode asynchronous sequential circuit given in Fig. 7.5.1.

Sol. : The given circuit has two input variables and Io and one output variable Z. The circuit has two feedback paths which provide inputs to the gates, creating latching operation necessary to produce a sequential circuit. The feedback path also generates the state variables X₀ and X₁ The next state for the circuit is determined by both, the state of input variables and the state variables.

Step 1 : Determine next-secondary state and output equations.

From the given sequential circuit we can have next-secondary state and output equations as follows

Step 2 : Construct state table.

• From these next-secondary state and output equations we can construct the state table indicating present-total state, next-total state, stability of the next-secondary state and the output. The next-secondary state values are found by assigning present-total state values to the Boolean variables in the next-secondary state equations to determine X⁺₁ and X⁺₀

• For the given input and secondary state if next-secondary state does not change then the state is said to be stable.

Note : The shaded portions show that for given inputs, next-secondary states do not match with the corresponding secondary states and hence they are unstable states.

The Fig. 7.5.2 shows the transition table. The numbers written in the table represent next-secondary state values for particular secondary state and inputs.

The circle around next-secondary state value indicate that the state is stable. The arrows indicate transitions from unstable states to stable states. For example, if the state (X₁ X₀, I₁ I₀) is 1010, the state value is 01 and it is unstable state. The next-secondary stable state will be 0010 as indicated by arrow. There is no stable state for input I₁ I₀ = 00 with secondary states 10 and 01.

Ex. 7.5.2 An asynchronous sequential circuit is described by the following excitation and output function.

Y = X₁X₂ + (X₁X₂) Y, Z = Y

i) Draw the logic diagram of the circuit.

ii) Derive the transition table and output map.

iii) Describe the behaviour of the circuit.

Sol. : i) The logic diagram is as shown in the Fig. 7.5.4 (a).

iii) The circuit gives carry output of the full adder circuit.

Ex. 7.5.3 An asynchronous sequential circuit has two internal states and one output. The excitation and output function describing the circuit are as follows.

Y₁ = x₁x₂ + x₁y₂+ x₂y₁  Y₂ = x₂ + x₁y₁y₂ + x₁, y₁ Z = x₂ + y₁

Sol. : The logic diagram is as shown in the Fig. 7.5.5 (a).

Ex. 7.5.4 Derive the flow table for the circuit given in the Fig. 7.5.6.

Sol. :

Step 1 : The excitation and output equations for the given circuit are :

Ex. 7.5.5 Consider the following asynchronous sequential circuit and draw maps, transition table and state table.

AU : Dec.-12, May-13, Marks 16

Sol. : Considering the excitation variables as outputs and the secondary variables as inputs we have,

Example for Practice

Ex. 7.5.6 Analyse the fundamental mode asynchronous sequential circuit shown in Fig. 7.5.10.

Review Questions

1. List and explain the steps used for analyzing an asynchronous sequential circuit.

AU : Dec.-10, Marks 8

2. State the condition of stability in asynchronous sequential logic.

3. List and explain the steps used for analyzing an asynchronous sequential circuit.

AU : May-12, 13, Marks 8

4. When does oscillation occur in an asynchronous sequential logic circuit ?