Ee2 chapter8 applicationsof_booleanalgebra

IT2001PA
Engineering Essentials (2/2)

Chapter 8 - Applications of Boolean
Algebra
Lecturer Name
lecturer_email@ite.edu.sg
Nov 20, 2012
Contact Number

Chapter 8 - Applications of Boolean Algebra

Lesson Objectives
Upon 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


Specific 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)


Example 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.



Example 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


 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



Example 2
 Write the Boolean equation for the circuit.

circuit.




 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


 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.



Example 3

circuit.




 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



X = BC + A
 To draw the simplified circuit, first write down the inputs
(A, B and C),and the output (X),



Example 4

circuit.




 X = (A+B)●B+(B)+(BC)



 Simplifying equation:
Boolean Equation at X: X = (A + B)●B + B + BC
Apply Distributive Law: X = AB + BB + B + BC
Apply (BB = 0): X = AB + 0 + B + BC
Apply (AB + 0) = AB: X = AB + B + BC
Since B is common for term 1 and term 2:X = B●(A + 1) + BC
Apply (A + 1) = 1: X = B ● 1 + BC
Apply (B●1) = B: X = B + BC
Apply (B +BC) = B+C: X=B+C



X=B+A
 To draw the simplified circuit, first write down the inputs (A,
B and C),and the output (X),



Example 5

circuit.




X = AB●(C+D)●AB

Simplifying Equation:

Boolean Equation at X: X= AB●(C+D)●AB
Apply Demorgan’s Thereom: X= AB + (C+D) + AB
Apply C+D = C+D: X= AB + C+D + AB
Apply AB + AB = AB: X= AB + C+D
Apply AB = A + B: X= A + B + C+D



X=A+B+C+D
 To draw the simplified circuit, first write down the inputs (A,
B,C and D), and the output (X),



Summary
 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.



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Ee2 chapter8 applicationsof_booleanalgebra

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