Computer Architecture and Organisation

Topic 4: Boolean Algebra

• LEARNING OUTCOMES

  By the end of this topics, you will be able to:

  1.      describe fundamental concept of Boolean Algebra, Boolean Functions, Truth Table and Algebraic manipulation of Boolean expressions.

  2.      simplify Boolean functions.

  3.      use Boolean function for correspondence with electronic circuits, combinational logic and sequential logic.

  4.      use sequential and clocked logic mutually exclusive projects.

  
  

  
  

  INTRODUCTION

  This topic explains about the fundamental of Boolean Algebra, Boolean functions, truth table and Algebraic manipulation of Boolean expressions.

  
  

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• Boolean Algebra
  

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• 

  
  

  
  

  Operator Name	Alternate Name	Example	Alternative Representations
  AND	Intersection logical multiplication	xy	x.y, x∩y, x&y, x∧y
  OR	Union logical addition	x + y	x∪y, x∨y
  NOT	Complement inversion	¬x	x’

  
  

  

  
  

  For example, the values of x∧y, x∨y, and ¬x can be expressed by tabulating their values with the following truth table:

  x	y	x∧y	x∨y	¬x	¬y
  0	0	0	0	1	1
  1	0	0	1	0	1
  0	1	0	1	1	0
  1	1	1	1	0	0

  
  LOGIC GATES

  
  

  
  

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• Lecture Note Topic 4: Boolean Algebra File

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• Self Check: Boolean Algebra

  
  

  1.      Use a truth table to simplify the following expressions:

  • (x.y) + (¬x.y)
  • (¬x.y).(x.y)

  2.      Use a Boolean Algebra to simplify the following truth tables:

  x	y	x∨y
  0	0	0
  1	0	1
  0	1	1
  1	1	1

  
  

  3. List THREE (3) basic logic gates.

  4. Draw a logic gate for the AND, OR and NOT logic operation.

  5. Draw a logic diagram for the following Boolean expressions:

  • (A + ^¬B + C) (^¬A + B + ^¬C)
  • (A + B + ^¬C) (A + B + ^¬C) (^¬A + ^¬B + ^¬C) 
  • ^¬A +((B + C)( ^¬B + ^¬C)

  
  

  Restricted Not available unless:

  • The activity Boolean Algebra is marked complete
  • The activity Lecture Note Topic 4: Boolean Algebra is marked complete
• Summary:

  In this topic you have learnt that:

  Fundamental concept of Boolean Algebra, Boolean Functions, Truth Table, Algebraic manipulation of Boolean expressions, Boolean functions, Boolean function for correspondence with electronic circuits, combinational logic, sequential logic, sequential and clocked logic mutually exclusive projects

  
  

  
  

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