Hazards in sequential circuits

Hazards

AU : Dec.-12, 14, 17, 18, May-16, 17

• The unwanted switching transients (glitches) that may appear at the output of a circuit are called Hazards. The hazards cause the circuit to malfunction. The main cause of hazards is the different propagation delays at different paths. Hazards occur in the combinational circuits, where they may cause a temporary false output value. When such combinational circuits are used in the asynchronous sequential circuits, they may result in a transition to a wrong stable state.

• There are two types of hazards : Static hazards and dynamic hazards. A static hazard exists if a signal is supposed to remain at particular logic value when an input variable changes its value, but instead the signal undergoes a momentary change in its required value. According to definition, the static hazards are further classified as static-0 hazard and static-1 hazard.

• In a combinational circuit, if output goes momentarily 0 when it should remain a 1, the hazard is known as static-1 hazard. On the other hand, if output goes momentarily 1 when it should remain a 0, the hazard is known as static-0 hazard. Another type of hazard is dynamic hazard in which output changes three or more times when it should change from 1 to 0 or from 0 to 1. The Fig. 8.1.1 shows the three types of hazards.

• The Fig. 8.1.2 shows circuit with hazards. Assume that, initially, inputs x₁ , x₂ and x₃ = 0. This causes the output of gate 1 to be 1, that of gate 2 to be 0, and the output of the circuit to be equal to 0. Now consider change in x₂ from 0 to 1. The output of gate 1 changes to 0 and that of gate 2 changes to 1, leaving the output at 0. However, the output momentarily goes to 1 if the propagation delay through the inverter is taken into consideration. The delay in the inverter causes the output of gate 2 to change to 1 before the output of gate 1 changes to 0. In this situation, both inputs of gate 3 are momentarily equal to 1, causing the output to go to 1 for the short time equal to the propagation delay of the inverter. This is illustrated in the Fig. 8.1.3.

 

1. Eliminating a Hazard

• The hazard exists because of the change of input results in a different product terms covering two minterms or different sum terms covering two maxterms. Whenever the circuit move from one product term to another or move one sum term to another, there is a possibility of a momentary interval when neither term is equal to 1, giving rise to an undesirable 0 output. Hazards can be eliminated by enclosing two minterms or maxterms in question. For example, if the circuit has minterms , then these two minterms must be enclosed by introducing another minterm x^. This is illustrated in Fig. 8.1.4.

 

Ex. 8.1.1 Find a way to remove the hazard in product of sums expression given by

AU : Dec.-12, Marks 4

Sol. :

Thus, we can eliminate hazard by adding one more OR gate as shown in Fig. 8.1.6.

 

Ex. 8.1.2 Give hazard-free realisation for the following Boolean function,

 f (A, B,C,D) = ^m (0, 2, 6, 7, 8, 10, 12)

Sol. : The given function can be implemented using K-map as shown in the Fig. 8.1.7 and Fig. 8.1.8 shows the additional product term, D overlapping two groups (group 1 and group 2) for hazard free realization. Group 1 and group 3 are already overlapped hence they do not require additional minterm for grouping.

2. Hazards in Sequential Circuits

• We know that, in sequential circuits, the combinational circuits are associated with them to drive the flip-flop inputs. In synchronous sequential circuits, the hazards due to combinational circuits associated with them are not of concern. This is because momentary erromeous signals are not generally troublesome in synchronous circuits. However, if a momentary incorrect signal is fed back in an asynchronous sequential circuit, it may cause the circuit to go to the wrong stable state.

• Let us consider the logic diagram and its transition table as shown in Fig. 8.1.9. For the circuit shown in Fig. 8.1.9, if the circuit is in total stable state YX₁X₂ = 111 and input X₂ changes from 1 to 0, the next total stable state should be YX₁X₂ = 110. However, because of hazard, the output Y may go to 0 momentarily. If this false signal feeds back into AND2 before the output of the inverter goes to 1, the output of AND2 will remain at 0 and the circuit will switch to the incorrect total stable state 010.

• Such a hazard can be eliminated by enclosing two minterms by another minterm as shown in the Fig. 8.1.10.

• Therefore, the hazard free asynchronous sequential circuit will be as shown in Fig. 8.1.11.

 

3. Essential Hazards

• In the previous section we have seen static and dynamic hazards and remedies to remove it. There is another type of hazard that may occur in asynchronous sequential circuits, called essential hazards. An essential hazard is caused by unequal delays along two or more paths that originate from the same input. Such hazards can be eliminated by adjusting the amount of delays in the affected path.

Review Questions

1. What are hazards in asynchronous sequential circuits ?

2. What are hazards in sequential circuits ? How can they be eliminated ?

AU : Dec.-12, Marks 6

3. Explain the various types of hazards in sequential circuit design and the methods to eliminate them. Give suitable examples.

4. What are static - 0 and static - 1 hazards? Explain the removal of hazards using hazard covers in K-map

AU : May-16, Marks 8

5. Illustrate about hazards in sequential circuits and the steps to avoid hazards in it.

AU : Dec.-18, Marks 13