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The Boolean equation X = [(A + B̅) (B + C)] B can be simplified to
- a)X = A̅B
- b)X = AB̅
- c)X = AB
- d)X = A̅ B̅
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The Boolean equation X = [(A + B) (B + C)] B can be simplified toa)X =...
X = [(A + B̅) (B + C)] B
= (AB + AC + 0 + B̅C)B
= AB + ABC
= AB(1 + C)
= AB
= (AB + AC + 0 + B̅C)B
= AB + ABC
= AB(1 + C)
= AB
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Community Answer
The Boolean equation X = [(A + B) (B + C)] B can be simplified toa)X =...
The Boolean equation X = [(A B) (B C)] B can be simplified to X = AB
Explanation:
To simplify the given Boolean equation, we need to apply the Boolean algebra rules and simplification techniques. Let's break down the equation step by step.
Step 1: Expand the equation
The given equation X = [(A B) (B C)] B can be expanded using the distributive property of Boolean algebra:
X = (A B) B + (B C) B
Step 2: Apply the AND operation
Using the AND operation (represented by a dot or no symbol), we can simplify the equation further:
X = AB + BB + BCB
Step 3: Simplify the equation
According to the Boolean algebra rules, the expression BB is always equal to B. Therefore, we can simplify the equation as follows:
X = AB + B + BCB
Step 4: Apply the OR operation
Using the OR operation (represented by a plus symbol), we can further simplify the equation:
X = AB + B(1 + CB)
Step 5: Simplify the expression within parentheses
The expression within parentheses can be simplified as follows:
1 + CB = 1 (since any value ORed with 1 results in 1)
Therefore, the equation becomes:
X = AB + B(1)
Step 6: Simplify the expression B(1)
Multiplying any expression with 1 results in the original expression. Therefore, we can simplify the expression as follows:
X = AB + B
Step 7: Simplify the equation
Using the distributive property, we can further simplify the equation:
X = AB + B = AB
Therefore, the simplified Boolean equation is X = AB.
Final Answer: The Boolean equation X = [(A B) (B C)] B can be simplified to X = AB.
Explanation:
To simplify the given Boolean equation, we need to apply the Boolean algebra rules and simplification techniques. Let's break down the equation step by step.
Step 1: Expand the equation
The given equation X = [(A B) (B C)] B can be expanded using the distributive property of Boolean algebra:
X = (A B) B + (B C) B
Step 2: Apply the AND operation
Using the AND operation (represented by a dot or no symbol), we can simplify the equation further:
X = AB + BB + BCB
Step 3: Simplify the equation
According to the Boolean algebra rules, the expression BB is always equal to B. Therefore, we can simplify the equation as follows:
X = AB + B + BCB
Step 4: Apply the OR operation
Using the OR operation (represented by a plus symbol), we can further simplify the equation:
X = AB + B(1 + CB)
Step 5: Simplify the expression within parentheses
The expression within parentheses can be simplified as follows:
1 + CB = 1 (since any value ORed with 1 results in 1)
Therefore, the equation becomes:
X = AB + B(1)
Step 6: Simplify the expression B(1)
Multiplying any expression with 1 results in the original expression. Therefore, we can simplify the expression as follows:
X = AB + B
Step 7: Simplify the equation
Using the distributive property, we can further simplify the equation:
X = AB + B = AB
Therefore, the simplified Boolean equation is X = AB.
Final Answer: The Boolean equation X = [(A B) (B C)] B can be simplified to X = AB.
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