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The minimised form of Boolean logic expression (A’B’C’ + A’BC’ + A’BC + ABC’) can be reduced to
- a)A’C’ + BC’ + A’B
- b)A’C’ + B’C’ + A’B
- c)A’C + BC + A’B
- d)AC + BC’ + AB
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The minimised form of Boolean logic expression (A’B’C&rsqu...
Given: A′B + ABC′ + BC’ + AB′C′
= A’B + BC’ (1 + A) + AB’C”
= A’B + BC’ + AB’C’
= A’B + BC’ + BC’ + AB’C’
= B(A’ + C’) + C’(A + AB’)
= B(AC)’ + C’ A(1 + B’)
= B(AC)’ + AC’.
= A’B + BC’ (1 + A) + AB’C”
= A’B + BC’ + AB’C’
= A’B + BC’ + BC’ + AB’C’
= B(A’ + C’) + C’(A + AB’)
= B(AC)’ + C’ A(1 + B’)
= B(AC)’ + AC’.
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The minimised form of Boolean logic expression (A’B’C&rsqu...
Understanding the Boolean Expression
To simplify the Boolean expression A’B’C’ + A’BC’ + A’BC + ABC’:
- Identify Variables: The variables involved are A, B, and C, with their respective complements (A’, B’, C’).
Step 1: Group Terms
- Group the terms based on common factors:
- A’B’C’ (all off)
- A’BC’ (A’ and C’ are common)
- A’BC (A’ common)
- ABC’ (B and C’ common)
Step 2: Factor Common Terms
- From the first two terms: A’B’C’ + A’BC’ = A’C’(B’ + B) = A’C’ (since B’ + B = 1)
- From the last two terms: A’BC + ABC’ = AC’ + A’B (after factoring)
Step 3: Combine the Results
- Combine the results from the previous step:
- Final expression = A’C’ + A’B + BC’
Final Simplified Expression
- The minimized form of the expression becomes:
- A’C’ + BC’ + A’B
Conclusion
- The correct simplified expression is A’C’ + BC’ + A’B, which matches option (a).
Thus, the minimized form of the given Boolean expression is indeed option A. This simplification demonstrates the effectiveness of Boolean algebra in reducing complex logic expressions.
To simplify the Boolean expression A’B’C’ + A’BC’ + A’BC + ABC’:
- Identify Variables: The variables involved are A, B, and C, with their respective complements (A’, B’, C’).
Step 1: Group Terms
- Group the terms based on common factors:
- A’B’C’ (all off)
- A’BC’ (A’ and C’ are common)
- A’BC (A’ common)
- ABC’ (B and C’ common)
Step 2: Factor Common Terms
- From the first two terms: A’B’C’ + A’BC’ = A’C’(B’ + B) = A’C’ (since B’ + B = 1)
- From the last two terms: A’BC + ABC’ = AC’ + A’B (after factoring)
Step 3: Combine the Results
- Combine the results from the previous step:
- Final expression = A’C’ + A’B + BC’
Final Simplified Expression
- The minimized form of the expression becomes:
- A’C’ + BC’ + A’B
Conclusion
- The correct simplified expression is A’C’ + BC’ + A’B, which matches option (a).
Thus, the minimized form of the given Boolean expression is indeed option A. This simplification demonstrates the effectiveness of Boolean algebra in reducing complex logic expressions.
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