Question

Boolean expression \[Y = A \cdot \bar B + B \cdot \bar A\] is given. If \[A = 1\], \[B = 1\] then \[Y = \]

Answer 1

Hint: Using the concept of Boolean operations, we will first calculate the unknown values that are required to find the value of Y. Later, we will substitute all the values in the given Boolean expression.

Complete step by step answer:Given:
The Boolean expression is \[Y = A \cdot \bar B + B \cdot \bar A\].
The value of the Boolean function A is 1.
The value of the Boolean function B is 1.

We know that if a Boolean function is true, then its value is given by unity, and if it is false, then it becomes zero. We are given that the value of function A and function B is unity, so the value of their inverse must be equal to zero so we can write:
\[\bar A = 0\]
And,
\[\bar B = 0\]

We will substitute 1 for A and B, 0 for \[\bar A\] , and \[\bar B\] in the given expression.
\begin{align*}
Y &= 1 \cdot 0 + 1 \cdot 0\\
 \Rightarrow Y &= 0 + 0\\
 \Rightarrow Y &= 0
\end{align*}

Additional information: We can understand that Boolean operations are logic statements, and their value could be correct or incorrect. There are many Boolean operations present; some of them are AND, OR, NAND, NOR, XNOR, etc. Each operator has its effect on the resultant of the circuit. Suppose the NOR gate is used at the end of a circuit, so it means that the result will be inverse of its earlier value. Depending on our requirement of the final result, we use different logic gates together.

Note:We can remember that the inverse of a Boolean operation whose value is true is given by zero to solve similar problems. We can use Boolean operations in logic gates’ value, which is a part of digital electronics.