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 ...
Chapter 19
HAZARDS AND PULSE MODE SEQUENTIAL CIRCUITS
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Lesson 2
Identification of Static Hazards
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Outline • Steps in identifying a static hazard • Example — NAND with delay at one of the input • Identification from Karnaugh map
Ch19L2-"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 • Ch19L2-"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
Ch19L2-"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
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Outline • Steps in identifying a static hazard • Example — NAND with delay at one of the input • Identification from Karnaugh map
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Steps • Y = X. X ; [X. X = 0, not allowed to be used for analyzing transient.] • Y = X + X; [Using DeMorgan theorem, get an OR expression. Modify further as OR expression not allowed for analyzing transient.] • Y = X + X.X; [Use rule X1.X1 = X1.] • Y = X1 + X2.X2; [Assume variable and its complement as separate variable.] Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Static 1 hazard from the Y Outputs • • • • •
When X1, X2 = 0, 0 the output = 0. When X1, X2 = 1, 0 the output = 1. When X1, X2 = 1, 1 the output = 1 When X1, X2 = 0, 1 the output = 1 Transient at X1, X2 = 0, 0
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Outline • Steps in identifying a static hazard • Example — NAND with delay at one of the input • Identification from Karnaugh map
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Step 3: Get SOP form of Boolean Expression • Draw two variable Karnaugh map by assuming the X0 and X0 as separate variables, X1 and X2.
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Map for Y
X2 X1
X2 X2 0
1
X1 0 X1 1
1
1
1
Dotted Line pairs present only during transient
Transient state = 0 Static 1 hazard Identified Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Static-0 Hazard X X'
Y X"
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Steps • Y = X' .X' • Y = X'. X' ; [X. X = 0, not allowed to be used for analyzing transient.] • Y = X' + X'; [Using DeMorgan theorem, get an OR expression. • Y = X1 + X2; [Assume variable and its complement as separate variable.]
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Static -0 hazard from the Y Outputs • • • • •
When X1, X2 = 0, 0 the output Y = 1. When X1, X2 = 1, 0 the output Y = 0. When X1, X2 = 1, 1 the output Y = 0 When X1, X2 = 0, 1 the output Y = 0 Transient at X1, X2 = 0, 0
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Map for Y
X2 X1 X1 1 X1 0
X2 X2 1 0
0 0
0
Dotted Line pairs present only during transient
Transient state = 1 Static 0 hazard Identified Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Summary
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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End of Lesson 2
Identification of Static Hazards
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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THANK YOU
Ch19L2-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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