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Determine the minimised expression of Boolean function
F = X̅ Z̅ + Y̅ Z̅ + Y Z̅ + XYZ
F = X̅ Z̅ + Y̅ Z̅ + Y Z̅ + XYZ
- a)X̅ Y̅ + Z
- b)Z̅ + XY
- c)X̅ Y + Z
- d)XYZ
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Determine the minimised expression of Boolean functionF = X Z + Y Z + ...
Concept:
All Boolean algebra laws are shown below
Calculation:
F = X̅ Z̅ + Y̅ Z̅ + Y Z̅ + XYZ
= X̅ Z̅ + Z̅ (Y̅ + Y) + XYZ
= X̅ Z̅ + Z̅ + XYZ
= Z̅ (1 + X̅) + XYZ
= Z̅ + XYZ
Now using Distributive Law
= (Z̅ + Z)(Z̅ + XY)
= Z̅ + XY
Calculation:
F = X̅ Z̅ + Y̅ Z̅ + Y Z̅ + XYZ
= X̅ Z̅ + Z̅ (Y̅ + Y) + XYZ
= X̅ Z̅ + Z̅ + XYZ
= Z̅ (1 + X̅) + XYZ
= Z̅ + XYZ
Now using Distributive Law
= (Z̅ + Z)(Z̅ + XY)
= Z̅ + XY
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Community Answer
Determine the minimised expression of Boolean functionF = X Z + Y Z + ...
To minimize the Boolean function F = X Z Y Z Y Z XYZ, we can use the laws of Boolean algebra to simplify the expression.
Starting with the given expression:
F = X Z Y Z Y Z XYZ
First, we can simplify the repeated terms Y Z Y Z to just Y Z:
F = X Z Y Z XYZ
Next, we can factor out Z from the first two terms:
F = Z(X + Y) XYZ
Now, we can distribute Z to both terms in the expression:
F = XZ + YZ XYZ
Finally, we can factor out XY from the last two terms:
F = XZ + YZ XY(Z + 1)
Since Z + 1 is always equal to 1, we can simplify the expression further:
F = XZ + YZ XY
Now, let's compare this simplified expression with the given options:
a) X Y Z: This option does not match the simplified expression.
b) Z XY: This option matches the simplified expression.
c) X Y Z: This option does not match the simplified expression.
d) XYZ: This option does not match the simplified expression.
Therefore, the correct answer is option 'B': Z XY.
Starting with the given expression:
F = X Z Y Z Y Z XYZ
First, we can simplify the repeated terms Y Z Y Z to just Y Z:
F = X Z Y Z XYZ
Next, we can factor out Z from the first two terms:
F = Z(X + Y) XYZ
Now, we can distribute Z to both terms in the expression:
F = XZ + YZ XYZ
Finally, we can factor out XY from the last two terms:
F = XZ + YZ XY(Z + 1)
Since Z + 1 is always equal to 1, we can simplify the expression further:
F = XZ + YZ XY
Now, let's compare this simplified expression with the given options:
a) X Y Z: This option does not match the simplified expression.
b) Z XY: This option matches the simplified expression.
c) X Y Z: This option does not match the simplified expression.
d) XYZ: This option does not match the simplified expression.
Therefore, the correct answer is option 'B': Z XY.
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Question Description
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