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Chapter 4Chapter 4
BOOLEAN ALGEBRA AND BOOLEAN ALGEBRA AND THEOREMS, MINI TERMS THEOREMS, MINI TERMS
AND MAXI TERMS AND MAXI TERMS
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
2
Lesson 1
BOOLEAN OPERATIONSBOOLEAN OPERATIONS
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
3
Outline
• Truth Table• NOT, AND, OR Operations• NAND, NOT Operations• XOR, NOT-XOR, NOT-NOT
operations
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
4
Table of n rows
A truth table has 2n rows for 2n
combination of n inputs. It gives in each of its row m outputs for a given combination. It gives the logic output(s) after the logical operations under different conditions of the input(s).
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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Example- Truth Table 2 input 1 output
0 0 1
Inputs Output A1 A2 F
0 1 01 0 01 1 0
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
6
Outline
• Truth Table•• NOT, AND, OR OperationsNOT, AND, OR Operations• NAND, NOT Operations• XOR, NOT-XOR, NOT-NOT
operations
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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NOT— 1 input 1 output
0 1
Input Output A F
1 0
Symbol
F= A
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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AND — 2 input 1 output
0 0 0
Inputs Output Inputs Y
0 1 01 0 01 1 1
SymbolF = A1. A2
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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OR— 2 input 1 output
0 0 0
Inputs Output A1 A2 F
0 1 11 0 11 1 1
SymbolF = A1+A2
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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NOT unique property is that output is high ‘1’ if input is at low ‘0’ logic level and output is low ‘0’ if input is at high ‘1’ logic level
Remember
AND unique property is that output is high ‘1’ only if all of the inputs are at high ‘1’logic levelOR unique property is that output is high ‘1’when any of the input is at high ‘1’ logic level
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
11
Outline
• Truth Table• NOT, AND, OR Operations•• NAND, NOR OperationsNAND, NOR Operations• XOR, NOT-XOR, NOT-NOT
operations
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
12
NAND — 2 input 1 output
0 0 1
Inputs Output A1 A2 Y
0 1 11 0 11 1 0
SymbolF = A1. A2
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
13
NOR— 2 input 1 output
0 0 1
Inputs Output A1 A2 F
0 1 01 0 01 1 0
SymbolF = A1+A2
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
14
NAND unique property is that output is high ‘1’ if any input is at low ‘0’ logic level and output is low ‘0’ if all inputs is at high ‘1’logic level
Remember
NOR unique property is that output is low ‘0’ when any of the input is at high ‘1’ logic level and output is low ‘1’ if all inputs is at high ‘0’ logic level
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
15
Outline
• Truth Table• NOT, AND, OR Operations• NAND, NO Operations•• XOR, NOTXOR, NOT--XOR, NOTXOR, NOT--NOT NOT
operationsoperations
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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XOR— 2 input 1 output
0 0 0
Inputs Output A1 A2 F
0 1 11 0 11 1 0
SymbolF = A1+A2
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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NOT-XOR— 2 input 1 output
0 0 1
Inputs Output A1 A2 F
0 1 01 0 01 1 1
SymbolF = A1+A2
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
18
NOT-NOT — 1 input 1 output
0 0
Inputs Output A F
1 0
Symbol
F = AOR
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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An XOR has unique property that the output is ‘1’ only if odd numbers of the input are ‘1’s.
Remember
A NOT-XOR has unique property that the output is ‘0’ only if odd numbers of the input are ‘1’s. NOT-NOT, also called Buffer — unique property is that output is at same logic level as input after a propagation delay
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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• NOT complements the input• AND give output 1 only when all inputs 1s• OR give output 0 only when all inputs 0s• NAND e give output 0 only when all inputs
1s• NOR give output 1 only when all inputs 0s• XOR give output 1 only odd number of
inputs 1s
Ch04L1-"Digital Principles and Design", Raj Kamal, Pearson Education, 2006
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End of Lesson 1
BOOLEAN OPERATIONSBOOLEAN OPERATIONS
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