Question
The simplified form of the Boolean function $F(A, B, C, D) = A\bar{B}C+ B+ B\bar{D} +AB\bar{D}+\bar{A}C$ is
The correct answer is
$B+C$
To simplify the given Boolean function \( F(A, B, C, D) = A\bar{B}C + B + B\bar{D} + AB\bar{D} + \bar{A}C \), we'll follow these steps:
- Identify and apply Boolean algebra rules to simplify the expression.
- Use the consensus theorem and absorption laws where applicable.
Simplification Process:
- Start with the expression: F = A\bar{B}C + B + B\bar{D} + AB\bar{D} + \bar{A}C
- Notice that B is present by itself in the expression, which implies that any terms ORed with B remain B due to absorption law: X + X = X and X + 1 = 1. Therefore, the expression simplifies to: F = B + \bar{A}C
- Examine if any further simplifications can be made: We see that \bar{A}C is not absorbed by B. Therefore, it simplifies to: B + C.
Conclusion:
The simplified form of the given Boolean function is B + C. Therefore, the correct answer is:
B + C
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Important Questions from Logic Gates and Boolean Algebra
In Boolean algebra, the term sum of products means
The value of \(\rm \overline{A+B}\) is :
- If A + B = A + C and AB = AC, then which of the following is true?
The Boolean function Y = AB + CD is to be realized using only two-input NAND gates. The minimum number of gates required are:
The minimum number of 2-input NAND gates required to realize the logic function $Y = AB + \bar A \bar B$ is
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