Question

Which logic gate is represented by the following combination of logic gates?

A. OR
B. NAND
C. AND
D. NOR

Answer 1

Firstly, identify the given gates and then recall their respective operations. Then, see what input goes into the third gate after passing through the gates at A and B terminals. From the output at Y terminal identify the gate that is represented by the given combination.

Complete answer:
We know that gate is a digital circuit that follows a logical relationship between input and the output voltages and also, they control the flow of information. Basically we have five common logic gates, namely, NOT, AND, OR, NAND and NOR. Each of them has a function that is defined by a truth table and also has a symbol. Truth tables help us in understanding the behavior of logic gates.
In the question three logic gates are given, namely, two NOT gates and one NOR gate. Before discussing their combination, let us discuss their individual functions.

NOT gate:
NOT gate is the most basic gate that has just one input and one output.

If we give 0 as input to this gate we get 1 as output and vice-versa. Clearly, here the output is the inverted version of input and hence it is called inverter. That is, if X was the input then the output is$\overline{X}$.
$X\Rightarrow \overline{X}$ ……………………………….. (1)

NOR gate:
This gate has two inputs and one output.

This gate is the combination of two functions: operation of OR gate followed by NOT gate. We get its output as 1 only when both its inputs are 0. Or we could say that if$X$and$Y$were the inputs then, the output of NOR-gate is given by, $\overline{X+Y}$
$X,Y\Rightarrow \overline{X+Y}$ ……………………………… (2)
So, for the combination, if $A$ and $B$ were the inputs then from (1) we have outputs as $\overline{A}$ and $\overline{B}$ respectively.
Now, the two inputs of NOR gate are $\overline{A}$ and$\overline{B}$, so from (2) we get the output as,
$\Rightarrow \overline{\overline{A}+\overline{B}}=\overline{\overline{A}\centerdot \overline{B}}$
$\Rightarrow \overline{\overline{A}}\centerdot \overline{\overline{B}}=A\centerdot B$ ………………………….. (3)
AND gate if you may recall has two or more inputs with just one output. The inputs have to be both 1 to give the output 1. That is, if X and Y were the inputs then output is given by,
$\Rightarrow X\centerdot Y$
Therefore, the combination given in the question results in it operating as an AND gate.

So, the correct answer is “Option C”.

Note:
In order to deal with questions involving logic gates, along with identifying the given gates, you should also know the resultant operation of the combination. For that you should learn the operations of all the five basic logic gates. Also, note that the NOR gate here is a universal gate, as it can obtain all the other gates using this.