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
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:
Important Questions from Logic Gates and Boolean Algebra
The number of distinct Boolean expressions of four variables is-
Which of the following types is best suited to represent the logical values?
In the given circuit, if the input voltage lies between +E1 and -E2, then output is zero.
Input and output characteristics are shown below.
The region between +E1 and -E2 is known as _____.
The minimum number of 2-input NAND gates required to realize the logic function $Y = AB + \bar A \bar B$ is
A*B*A, where * represents XOR, is equal to:
