circuits mode sequential hazards and …digital principles and design", raj kamal, pearson...

Ch19L5-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006 1

Chapter 19

HAZARDS AND PULSE MODE SEQUENTIAL

CIRCUITS


Lesson 5

Dynamic Hazards, Essential Hazards and Pulse mode sequential circuits


Outline

• Dynamic Hazards• Essential Hazard• Pulse Mode Sequential circuit


Hazard Free Circuit• Elimination static-0 and static-1 hazards —

each variable, which is used as the input at any stage after adding the terms that eliminates the static hazards are used in only one form: either as such or complement form, then the circuit is hazard free. However, dynamic hazards may still be present. If we remove dynamic hazards, the we get hazard free circuit.


Dynamic Hazard• When an output though suppose to

undergo transition only once if changes total (2n + 1) times, where n = 1 or 2 or 3 and so on, there is a dynamic hazard. The n is the number of times the output toggle back to initial value. Dynamic hazards arise due to later stage gates undergoing the transitions slower than the previous stage gates or vice versa


Dynamic Hazard

Y

X

X

t

5 times changes Hazard

∆t

∆t'

Static Hazard Eliminated


Dynamic Hazard Source

• Circuit 1 inputs are also inputs to next stage circuit 2

circuit 1 circuit 2


Outline



Asynchronous sequential circuit

• Consider asynchronous sequential circuit. Let us assume that (i) Static hazards have been eliminated (ii) Dynamic hazard has been eliminated (iii) Races that are critical has been eliminated (iv) The circuit operates in fundamental mode so that the input is changed only after a stable state is reached


Essential Hazard • Due to different instances at which change

in the excitation variable yq occurs when there is a change in an input variable Xi.

• Essential hazard arises out that an input variable affects the different feedback cycle variables at different instances. Before the expected set of all yq excitation input changes finish, the state variable(s) xq can change, which may lead to circuit not functioning as expected


Excitation-cum-Transition Table for Y = X. xq2 + xq1;

xq1’ =D and xq2’ = xqn+1 = J. xq n + K. xq n

State Transition Outputs Y (xq0, xq1) [xq0’, xq1’]X=0 [xq0’, xq1’]X=1 X=0 X =1

(0, 0) 0, 0 1, 0 0 0

� (0, 1) 0, 1 1, 0 1 0(1, 0) 0, 1 1, 1 1 1

� (1, 1) 0, 1 0, 0 1 1


Essential Hazard Source

X Combination circuit 1Combination circuit 2

Latch 1

Latch 2XQ

YQ

Y


Essential hazard in an asynchronous sequential circuit operation

• When an input variable affects the different feedback cycle excitation variables at the different instances.

• Introduction of the additional delays greater than the delays in the combination circuits providing the excitations in the feedback cycles eliminates essential hazard.


Outline



Pulse Mode Sequential Circuit

X Combination circuit 1Combination circuit 2

FF 1

FF 2XQ

YQ

Y

ClockPulses

or sequential circuit

∆t


Essential hazard Elimination

• When the period ∆T of the clock pulse, which excite a synchronous sequential circuit is greater than the time periods during which an input variable(s) affects the different feedback cycle excitation variables, the circuit will be free from essential hazards.


Summary


• Dynamic hazards due to next stage getting input, which is common to a previous stage input and when number of output changes are odd

• Essential hazard due to delays in different latches or FFs are different

• Pulse clocked sequential circuit is free from essential hazards when pulse interval is more than the time required for number of feedback cycles to get a stable output.


End of Lesson 5

Dynamic Hazards, Essential Hazards and Pulse mode

sequential circuits


THANK YOU

circuits mode sequential hazards and …digital principles and design", raj kamal, pearson...

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