Question

The combination of gates below equivalent to:

(A) AND gate
(B) XOR gate
(C) NOR gate
(D) NAND gate

Answer 1

Hint: Logic gates can be defined as an electronic component which can be used to conduct electricity based on the rule implementing the logical operation performed on one or more binary inputs which produces the single binary output. Here we are asked to find the type of the logic gate used by using the inputs given and resultant output data.

Complete answer:
Here, we are given inputs A and B which are applied through the NOT gate with bubbles which means the output would be inverted, that is it will be $ \overline A $ and $ \overline B $ .
Secondly the inputs $ \overline A $ and $ \overline B $ are passed through the NOR gate which gives the output as $ Y = \overline {\overline A + \overline B } $ and by using the properties of Boolean algebra –
 $ Y = \overline {\overline A + \overline B } = \overline{\overline {AB}} = AB $
Since, inverted to inverted cancels each other.
Now, at the last this output is applied as input through the NOT gate and gives –
 $ {Y_f} = \overline {AB} $
This is the output for the NAND gate.
Hence, from the given multiple choices – the option D is the correct answer.

Additional Information:
XOR
XOR gate can be defined as the digital logic gate which gives a true ( $ 1 $ ) or high output when the number of true inputs is odd. It is the hybrid gate which is the combination of the multiplication and the addition.
NAND
NAND gate can be defined as the digital logic gate which produces an output which is false $ (0) $ only if all the inputs are true.
NOR
NOR gate can be defined as the digital logic gate which gives a true ( $ 1 $ ) or high output when the both the inputs are low and if one or both the input is high then low output results.
OR
OR gate can be defined as the digital logic gate which gives a true ( $ 1 $ ) or high output if both the inputs are high and if neither input is high then a low output result.

Note:
Remember the comparative statement for all the logic gates for the inputs high or low and the resulting output low and high. High means one and low means zero inputs/ outputs.