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Title: BOOLEAN ALGEBRA notes
Description: Providing complete details about the Boolean algebra with good vocabulary and solutions,examples.
Description: Providing complete details about the Boolean algebra with good vocabulary and solutions,examples.
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COE 202: Digital Logic Design
Combinational Logic
Part 1
Dr
...
• What is inside the gate is not of concern to the
system/computer designer (Only its function)
• Binary logic (Boolean Algebra ) is a mathematical system
to analyze and design digital circuits
– George Boole (introduced mathematical theory
of logic in1854)
Ahmad Almulhem, KFUPM 2009
Boolean Algebra
Regular Algebra
Boolean Algebra
Values
Numbers
Integers
Real numbers
Complex Numbers
1 (True, High)
0 (False, Low)
Operators
+, -, x, /, … etc
AND (
...
Ahmad Almulhem, KFUPM 2009
Logical Operations
Three basic logical operations can be applied to binary
variables:
AND: Z = X
...
Y
0
0
0
0
1
0
1
0
0
1
1
1
Ahmad Almulhem, KFUPM 2009
Similar to
multiplication
AND Gate
The electronic device that performs the AND operation is
called the AND gate
X
Z
Y
An AND gate with two input variables X, Y and one output Z
Note: The output of the AND gate Z is a 1 if and only if all
the inputs are 1 else it is 0
Ahmad Almulhem, KFUPM 2009
3-input AND gate
Truth Table for a 3 input AND gate
W
X
Z
Y
Note: For an n-input logic gate,
the size of the truth table is 2n
W
X
Y
Z
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
Ahmad Almulhem, KFUPM 2009
OR Operation
The truth table for the OR logical operation
OR
X
Y
Z = X +Y
0
0
0
0
1
1
1
0
1
1
1
1
Ahmad Almulhem, KFUPM 2009
Similar to
addition
OR Gate
The electronic device that performs the AND operation is
called the AND gate
X
Y
Z
An OR gate with two input variables X, Y and one output Z
Note: The output of the OR gate Z is a 1 if either of the two
inputs X, Y are 1
Ahmad Almulhem, KFUPM 2009
OR Gate – 3 Input
Truth Table for a 3 input OR gate
W
X
Z
Y
Note: For an n-input logic gate,
the size of the truth table is 2n
W
X
Y
Z=W+X+Y
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
Ahmad Almulhem, KFUPM 2009
NOT Operation
•NOT is a unary operator, meaning there can only be 1 input
•The NOT operation can be represented as follows: Z= X’ or
Z=X
•X is also referred to as the complement of Z
...
Boolean expressions are fully defined by their truth tables
A Boolean expression can be represented using interconnected logic
gates
– Literals correspond to the input signals to the gates
– Constants (1 or
Title: BOOLEAN ALGEBRA notes
Description: Providing complete details about the Boolean algebra with good vocabulary and solutions,examples.
Description: Providing complete details about the Boolean algebra with good vocabulary and solutions,examples.