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Ee2 chapter8 applicationsof_booleanalgebra

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Ee2 chapter8 applicationsof_booleanalgebra

  1. 1. IT2001PAEngineering Essentials (2/2)Chapter 8 - Applications of BooleanAlgebra Lecturer Namelecturer_email@ite.edu.sg Nov 20, 2012Contact Number
  2. 2. Chapter 8 - Applications of Boolean AlgebraLesson ObjectivesUpon completion of this topic, you should be able to: Apply Boolean algebra to solve combination logic of up to 2 variables. IT2001PA Engineering Essentials (2/2) 2
  3. 3. Chapter 8 - Applications of Boolean AlgebraSpecific Objectives Students should be able to :  Determine the output logic expression from a given logic circuit.  Use Boolean algebra to simplify logic expressions. IT2001PA Engineering Essentials (2/2)
  4. 4. Chapter 8 - Applications of Boolean AlgebraExample 1 Write the Boolean equation for the circuit Use DeMorgan’s Theorem and then Boolean Algebra rules to simplify the equation. Draw the simplified circuit. IT2001PA Engineering Essentials (2/2) 4
  5. 5. Chapter 8 - Applications of Boolean AlgebraExample 1 (Solution) Boolean equation at X, X = (AB)●B Apply De Morgan’s X = (A + B) ● B theorem: (Use parentheses, () to maintain proper grouping) Apply Distributive X = AB + BB Law: Apply Boolean Algebra = AB + 0 rule: = AB IT2001PA Engineering Essentials (2/2) 5
  6. 6. Chapter 8 - Applications of Boolean AlgebraExample 1 (Solution) The simplified equation will be X=AB To draw the simplified circuit, first write down the inputs (A and B), and the output (X), then insert the corresponding gates IT2001PA Engineering Essentials (2/2) 6
  7. 7. Chapter 8 - Applications of Boolean AlgebraExample 2 Write the Boolean equation for the circuit. Use DeMorgan’s Theorem and then Boolean Algebra rules to simplify the equation. Draw the simplified circuit. IT2001PA Engineering Essentials (2/2) 7
  8. 8. Chapter 8 - Applications of Boolean AlgebraExample 2 (Solution) X = B●(A+C)+C, Simplifying equation: Boolean Equation at X: X = B●(A + C) + C Apply Distributive Law: X = BA + BC + C Since C is common for term 2 and term 3: X = BA + C●(B + 1) Apply (B + 1) = 1: X = BA + C● 1 Apply C●1 = C: X = BA + C Apply BA = AB: X = AB + C IT2001PA Engineering Essentials (2/2) 8
  9. 9. Chapter 8 - Applications of Boolean AlgebraExample 2 (Solution) The simplified equation will be: X = AB + C To draw the simplified circuit, first write down the inputs (A, B and C),and the output (X), then insert the corresponding gates. Finally, join the gates. IT2001PA Engineering Essentials (2/2) 9
  10. 10. Chapter 8 - Applications of Boolean AlgebraExample 3 Write the Boolean equation for the circuit. Use DeMorgan’s Theorem and then Boolean Algebra rules to simplify the equation. Draw the simplified circuit. IT2001PA Engineering Essentials (2/2) 10
  11. 11. Chapter 8 - Applications of Boolean AlgebraExample 3 (Solution) X = (A+B)●BC+A Simplifying equation: Boolean Equation at X: X = (A+B) ● BC + A Apply Distributive Law: X = ABC + BBC + A Apply BBC = BC: X = ABC + BC+ A Since BC is common for term 1 and term 2: X = BC (A +1) + A Apply (A + 1) = 1: X = BC + A IT2001PA Engineering Essentials (2/2) 11
  12. 12. Chapter 8 - Applications of Boolean AlgebraExample 3 (Solution) The simplified equation will be: X = BC + A To draw the simplified circuit, first write down the inputs (A, B and C),and the output (X), then insert the corresponding gates. Finally, join the gates. IT2001PA Engineering Essentials (2/2) 12
  13. 13. Chapter 8 - Applications of Boolean AlgebraExample 4 Write the Boolean equation for the circuit. Use DeMorgan’s Theorem and then Boolean Algebra rules to simplify the equation. Draw the simplified circuit. IT2001PA Engineering Essentials (2/2) 13
  14. 14. Chapter 8 - Applications of Boolean AlgebraExample 4 (Solution) X = (A+B)●B+(B)+(BC) IT2001PA Engineering Essentials (2/2) 14
  15. 15. Chapter 8 - Applications of Boolean AlgebraExample 4 (Solution) Simplifying equation:Boolean Equation at X: X = (A + B)●B + B + BCApply Distributive Law: X = AB + BB + B + BCApply (BB = 0): X = AB + 0 + B + BCApply (AB + 0) = AB: X = AB + B + BCSince B is common for term 1 and term 2:X = B●(A + 1) + BCApply (A + 1) = 1: X = B ● 1 + BCApply (B●1) = B: X = B + BCApply (B +BC) = B+C: X=B+C IT2001PA Engineering Essentials (2/2) 15
  16. 16. Chapter 8 - Applications of Boolean AlgebraExample 4 (Solution) The simplified equation will be: X=B+A To draw the simplified circuit, first write down the inputs (A, B and C),and the output (X), then insert the corresponding gates. Finally, join the gates. IT2001PA Engineering Essentials (2/2) 16
  17. 17. Chapter 8 - Applications of Boolean AlgebraExample 5 Write the Boolean equation for the circuit. Use DeMorgan’s Theorem and then Boolean Algebra rules to simplify the equation. Draw the simplified circuit. IT2001PA Engineering Essentials (2/2) 17
  18. 18. Chapter 8 - Applications of Boolean AlgebraExample 5 (Solution) X = AB●(C+D)●ABSimplifying Equation:Boolean Equation at X: X= AB●(C+D)●ABApply Demorgan’s Thereom: X= AB + (C+D) + ABApply C+D = C+D: X= AB + C+D + ABApply AB + AB = AB: X= AB + C+DApply AB = A + B: X= A + B + C+D IT2001PA Engineering Essentials (2/2) 18
  19. 19. Chapter 8 - Applications of Boolean AlgebraExample 5 (Solution) The simplified equation will be: X=A+B+C+D To draw the simplified circuit, first write down the inputs (A, B,C and D), and the output (X), then insert the corresponding gates. Finally, join the gates. IT2001PA Engineering Essentials (2/2) 19
  20. 20. Chapter 8 - Applications of Boolean AlgebraSummary Steps taken to simplify a combination logic circuit:  Write down the expression of a given Combination Logic Circuit.  Simplify the expression using Boolean Algebra Theorem.  Draw the Logic Circuit using the simplified Logic Expression. IT2001PA Engineering Essentials (2/2) 20
  21. 21. Chapter 8 - Applications of Boolean AlgebraNext Lesson IT2001PA Engineering Essentials (2/2) 21

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