The Boolean expression for NOR gate is:
A. $\overline {A \cdot B} = Y$
B. $A + B = Y$
C. $A \cdot B = Y$
D. $\overline {A + B} = Y$

Hint: We know that there are different types of logic gates which are used in digital structures. There are mainly three gates: OR gate, AND gate and NOT gate and by combining these in different ways, we can get logic gates such as NOR gate and NAND gate. Here, we need to know the combination of NOR gate to determine its Boolean expression.

Complete step by step answer:
First, we will see the definition of NOR gate. The NOR gate his means that in NOR gate, only high output signal is obtained when there are low signals on the inputs.
Let us now see the logic circuit and symbol of NOR gate as per its definition:

From the logic circuit, we can obtain the Boolean expression for NOR gate.
First for the OR gate in the circuit, the output becomes $A + B$ and after the NOT get, we get $\overline {A + B} $ as our final output.
If we say $Y$ is our final output, then the equation becomes $\overline {A + B} = Y$. This equation is called the Boolean expression for NOR gate.
We can read the equation as “$Y$ equals to NOT $A$ OR $B$”
The output of NOR gate can be only high when both the inputs are low because in this gate, an OR gate is followed by a NOT gate.

So, the correct answer is “Option D”.


Note:
We have seen the Boolean expression of NOR gate. Now let us consider the other options given in the question.
The first option, $\overline {A \cdot B} = Y$is the Boolean expression of NAND gate,
The second option, $A + B = Y$is the Boolean expression of OR gate, and
The third option, $A \cdot B = Y$is the Boolean expression of AND gate.