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By simplifying the given Boolean function, Y = ABC + A'B + ABC' + AC, the minimum number of literals is
- a)3
- b)4
- c)6
- d)7
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
By simplifying the given Boolean function, Y = ABC + A'B + ABC' + AC,...
Given Boolean function:
Y = ABC + A'B + ABC' + AC
Simplifying the Boolean function:
To simplify the given Boolean function, we can use various Boolean algebra laws and rules such as the distributive law, De Morgan's law, and complement law.
Applying the distributive law:
Y = ABC + A'B + ABC' + AC
= AB(C + C') + A'B + AC
= AB + A'B + AC
Applying the complement law:
Y = AB + A'B + AC
= AB + A'B + AC + (A + A')(B + B')(C + C')
= AB + A'B + AC + AB'C' + AB'C + A'BC + A'BC'
= AB + AB'C' + AB'C + A'BC + A'BC' + A'B + AC
Grouping the common terms:
Y = AB(1 + C' + C) + A'B(1 + C + C') + AC(1 + B)
= AB(1) + A'B(1) + AC(1)
= AB + A'B + AC
Reduced Boolean function:
Y = AB + A'B + AC
Minimum number of literals:
The minimum number of literals in the reduced Boolean function is the sum of the number of literals in each term. In this case, each term has 2 literals.
Y = AB + A'B + AC
Therefore, the minimum number of literals is 2 + 2 + 2 = 6.
Conclusion:
The minimum number of literals in the simplified Boolean function Y = ABC + A'B + ABC' + AC is 6. Therefore, the correct answer is option 'C'.
Y = ABC + A'B + ABC' + AC
Simplifying the Boolean function:
To simplify the given Boolean function, we can use various Boolean algebra laws and rules such as the distributive law, De Morgan's law, and complement law.
Applying the distributive law:
Y = ABC + A'B + ABC' + AC
= AB(C + C') + A'B + AC
= AB + A'B + AC
Applying the complement law:
Y = AB + A'B + AC
= AB + A'B + AC + (A + A')(B + B')(C + C')
= AB + A'B + AC + AB'C' + AB'C + A'BC + A'BC'
= AB + AB'C' + AB'C + A'BC + A'BC' + A'B + AC
Grouping the common terms:
Y = AB(1 + C' + C) + A'B(1 + C + C') + AC(1 + B)
= AB(1) + A'B(1) + AC(1)
= AB + A'B + AC
Reduced Boolean function:
Y = AB + A'B + AC
Minimum number of literals:
The minimum number of literals in the reduced Boolean function is the sum of the number of literals in each term. In this case, each term has 2 literals.
Y = AB + A'B + AC
Therefore, the minimum number of literals is 2 + 2 + 2 = 6.
Conclusion:
The minimum number of literals in the simplified Boolean function Y = ABC + A'B + ABC' + AC is 6. Therefore, the correct answer is option 'C'.
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Community Answer
By simplifying the given Boolean function, Y = ABC + A'B + ABC' + AC,...
Y = ABC + A'B + ABC' + AC
= AB(C + C') + A'B + AC
= AB + A'B + AC = (A + A')B + AC = B + AC
So, the number of literals is 3.
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By simplifying the given Boolean function, Y = ABC + A'B + ABC' + AC, the minimum number of literals isa)3b)4c)6d)7Correct answer is option 'A'. Can you explain this answer?
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