The logical addition (+) symbol is placed between two variables, say
A and B
0 + 0 = 0
0 + 1 =1
1 + 0 = 1
1 + 1 = 1
The plus symbol (+) read as "OR", therefore A +B is read as A OR B
The logical addition (.) symbol is placed between two variables, say A
and B
0 . 0 = 0
0 . 1 =0
1 . 0 = 0
1 . 1 = 1
The plus symbol (.) read as “AND", therefore A .B is read as AAND B
The commutative law for addition and multiplication of two variables
is written as,
A + B = B + A
& A . B = B . A
The associative law for addition and multiplication of three variables
is written as,
(A + B) + C = A + (B + C)
& (A .B) . C = A. (B. C)
The distributive law for three variables involves, both addition
& multiplication and is written as,
A (B+ C) = A B + AC
A logic gate is defined as a electronics circuit with two or more input
signals and one output signal. These gates are classified into two
types
• Basic Gates
• Derived Gates
There are three basic gates. They are
• OR gate
• AND gate
• NOT gate
It is a basic gate which will have multiple inputs and one output. It is
represented by the symbol ‘+’
Output of the OR gate will be high when any one of the input is high
It is a basic gate which will have multiple inputs and one output. It is
represented by the symbol ‘.’
Output of the AND gate will be high when all the inputs are high
It is a basic gate which will have one input and one output. It is
represented by ‘_’
Output of the NOT gate will be complement of input
• The positive logic
• The negative logic

I Semester-Unit 3 Boolean Algebra.pptx

  • 3.
    The logical addition(+) symbol is placed between two variables, say A and B 0 + 0 = 0 0 + 1 =1 1 + 0 = 1 1 + 1 = 1 The plus symbol (+) read as "OR", therefore A +B is read as A OR B The logical addition (.) symbol is placed between two variables, say A and B 0 . 0 = 0 0 . 1 =0 1 . 0 = 0 1 . 1 = 1 The plus symbol (.) read as “AND", therefore A .B is read as AAND B
  • 4.
    The commutative lawfor addition and multiplication of two variables is written as, A + B = B + A & A . B = B . A The associative law for addition and multiplication of three variables is written as, (A + B) + C = A + (B + C) & (A .B) . C = A. (B. C) The distributive law for three variables involves, both addition & multiplication and is written as, A (B+ C) = A B + AC
  • 5.
    A logic gateis defined as a electronics circuit with two or more input signals and one output signal. These gates are classified into two types • Basic Gates • Derived Gates There are three basic gates. They are • OR gate • AND gate • NOT gate
  • 6.
    It is abasic gate which will have multiple inputs and one output. It is represented by the symbol ‘+’
  • 7.
    Output of theOR gate will be high when any one of the input is high
  • 8.
    It is abasic gate which will have multiple inputs and one output. It is represented by the symbol ‘.’
  • 9.
    Output of theAND gate will be high when all the inputs are high
  • 10.
    It is abasic gate which will have one input and one output. It is represented by ‘_’ Output of the NOT gate will be complement of input
  • 12.
    • The positivelogic • The negative logic