Chapter 19
HAZARDS AND PULSE MODE
SEQUENTIAL CIRCUITS
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
1
Lesson 3
Identification of Static Hazards—
Part 2
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Outline
• Identification from Karnaugh map
• Absence of Static 1 from POS form
Boolean Expression
• Absence of Static 0 from SOP Form
Boolean Expression
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Step 1: Write Boolean expression
• Write Boolean expression for the logic
circuit and assume variable X and its
complement as two separate variables
without using the Boolean laws X +
X = 1 and X. X = 0
•
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Step 2a: Get SOP form of Boolean
Expression
• Write Boolean expression in POS form
using two variables without using the
Boolean laws X + X = 1 and X. X =
0
• Identify the static 1 hazard
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Step 2b: Get POS form of Boolean
Expression
• Write Boolean expression in POS form
using two variables and without using
the Boolean laws X + X = 1 and X.
X = 0
• Identify the static 0 hazard
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Step 3: Get SOP form of Boolean
Expression
• Draw three variable Karnaugh map by
assuming the X0 and X0 as separate
variables, X1 and X2 or X2 and X3 .
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Step 4: Get SOP form of Boolean
Expression
• Find a pairs of diads with no
overlapping between two diads.
• Consider when we change from
adjacent column to another or adjacent
row to another, there is a single
variable change. If in the given logic
circuit, that path does not exist, then a
static hazard arises
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Map for Y = (X2. X3) + (X1. X2)
Transient
X3
X3 X3 state = 0
X1 X2
0
1
Static 1
hazard
X1.X2 00
Identified.
Path does not
1
1
X1.X2 10
exists
between two
X1.X2 11
1
diads.
1
X1.X2 01
X2 . X3 Not
present.
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Map for Y = (X1+X2) . (X1+X3)
Transient
X3
X3 X3 state = 1
X1+X2
1
0
Static 0
hazard
0
0
X1 + X200
Identified.
Path does not
X1 + X2 01
exists
between two
0
X1 + X2 00
diads.
0
X1 + X210
X2 +X3
Not present.
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Outline
• Identification from Karnaugh map
• Absence of Static 1 from POS form
Boolean Expression
• Absence of Static 0 from SOP Form
Boolean Expression
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Absence of static 1
• If a Boolean expression has a term
present in POS with either a variable or
its complement only, then static-1
hazard is ruled out. This is however
does not mean that if a variable as well
as complement occur in the expression,
then static-0 hazard may or may not be
present. Presence can then be detected
by Karnaugh map in POS form.
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Example 1
• Y= (X1+X2 ).(X2+ X3);
[Complements of X1, X3 and X2 are
not existing. So static-1 hazard ruled
out.]
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Example 2
• Y = (X1 + X3). (X1 + X2).(X2 +
X3); [Complements of X1, X3 and
X2 are not existing. So static-1 hazard
ruled out.]
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Example 3
• Y = (X1 + X3). (X1 + X3 + X2).(X2
+ X3);
[Complements of X1, and
X2 are existing. So static-1 hazard not
ruled out.]
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Outline
• Identification from Karnaugh map
• Absence of Static 1 from POS form
Boolean Expression
• Absence of Static 0 from SOP Form
Boolean Expression
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Absence of static 0
• If a Boolean expression has a term
present in SOP with either a variable or
its complement only, then static-0
hazard is ruled out. This is however
does not mean that if a variable as well
as complement occur in the expression,
then static-1 hazard may or may not be
present. Presence can then be detected
by Karnaugh map in SOP form.
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Example 1
• Y= (X1.X2 )+ (X2 . X3);
[Complements of X1, X3 and X2 are
not existing. So static-0 hazard ruled
out.]
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Example 2
• Y = (X1 . X3)+ (X1 . X2) + (X2 .
X3); [Complements of X1, X3 and
X2 are not existing. So static-0 hazard
ruled out.]
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Example 3
• Y = (X1 . X3)+ (X1 . X3 . X2) +(X2
+ X3);
[Complements of X1, and
X2 are existing. So static-1 hazard not
ruled out.]
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Summary
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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• Draw Karnaugh map and Static 0
Hazard is found from POS form by
considering pair of diads with a
missing term, which makes a quad.
• Draw Karnaugh map and Static 1
Hazard is found from SOP form by
considering pair of diads with a
missing term, which makes a quad.
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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• If a POS form contains variables in one
form only, either a variable or its
complement form, then static 1 hazard
rules out
• If an SOP form contains variables in
one form only, either a variable or its
complement form, then static 0 hazard
rules out
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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End of Lesson 3
Identification of Static Hazards—
Part 2
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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THANK YOU
Ch19L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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