Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will...
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Transcript of Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will...
![Page 1: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/1.jpg)
Lecture 4Introduction to Boolean Algebra
![Page 2: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/2.jpg)
Binary Operators
In the following descriptions, we will let A and B be Boolean variables and define a set of binary operators on them. The term binary in this case does not refer to base-two arithmetic but rather to the fact that the operators act on two operands.
unary operator NOT
binary operators AND, OR, NAND, XOR
![Page 3: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/3.jpg)
Logic Gates
NOT
AND
OR
XOR
NAND
NOR
![Page 4: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/4.jpg)
F(A,B,C) = A + BC'
Truth Tables
A B C C' BC' A+BC'
0 0 0 1 0 0
0 0 1 0 0 0
0 1 0 1 1 1
0 1 1 0 0 0
1 0 0 1 0 1
1 0 1 0 0 1
1 1 0 1 1 1
1 1 1 0 0 1
![Page 5: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/5.jpg)
A Boolean Function Implemented in a Digital Logic Circuit
![Page 6: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/6.jpg)
Pow
er S
uppl
y
Input = 1 1 0
Voltmeter
NOT gates AND gates
OR gate(s)
The Part of the Circuit Usually Not Shown
![Page 7: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/7.jpg)
A One-Bit Adder Circuit
![Page 8: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/8.jpg)
Venn Diagrams
A A B A B
A B A BA B
A
~A + B
A .BA+B
A .BA=B
A A B A B
A B A BA B
A
~A + B
A .BA+B
A .BA .BA=B
![Page 9: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/9.jpg)
Three-Variable Venn Diagram
F(A,B,C) = A + BC'
000
001
010
011
100
101
110
111
A B
C
A B
C
![Page 10: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/10.jpg)
De Morgan's Theorem
BABA
BABA
A B A+B ~(A+B) ~A ~B (~A).(~B) ~(A+B)=(~A).(~B)
0 0 0 1 1 1 1 1
0 1 1 0 1 0 0 1
1 0 1 0 0 1 0 1
1 1 1 0 0 0 0 1
A B A+B ~(A+B) ~A ~B (~A).(~B) ~(A+B)=(~A).(~B)
0 0 0 1 1 1 1 1
0 1 1 0 1 0 0 1
1 0 1 0 0 1 0 1
1 1 1 0 0 0 0 1
![Page 11: Lecture 4 Introduction to Boolean Algebra. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of.](https://reader036.fdocuments.in/reader036/viewer/2022082613/5697bfed1a28abf838cb8d38/html5/thumbnails/11.jpg)
Textbook Reading for Chapter 4