Question

The given electrical network is equivalent to ?

A) AND gate
B) OR gate
C)NOR gate
D) NOT gate

Answer 1

Hint: In the above mentioned electrical network we can see that one nand gate and 2nor gate are used .NAND gate is a combination of AND and NOT gate and NOR gate is a combination of digital OR gate and an inverter or NOT gate connected together NAND and NOR gates are universal gates and also economical.

Complete answer:
NAND gate
Nand gate is a combination of an AND gate and NOT gate ,they are connected in cascade form it is also called negated and gate
NAND gate is represented as below

Boolean expression of NAND gate is
$output(y)=\overline{A.B}$
Truth table

A	B	Y
0	0	1
0	1	1
1	0	1
1	1	0

NOR Gate
NOR gate is a combination of digital OR gate and an inverter or NOT gate connected together NAND and NOR gates are universal gates and also economical.
NOR gate is represented as below

Boolean expression of NOR gate
$y=\overline{A+B}$
Truth table

A	B	Y
0	0	1
0	1	0
1	0	0
1	1	0

In the above electrical network the input $A$ enter the NAND gate and the output of NAND gate is $\overline{A}$
Input $B$ enters the NOR gate and the output of NOT gate is $\overline{B}$
In the electrical network the output of both NAND gate and nor gate is given as input to NOR gate
$Y=\overline{\overline{A}+\overline{B}}$
From DeMorgan’s Second theorem
$\overline{\overline{A}+\overline{B}}=A.B$
The final output is $A.B$
Which is the output of AND gate

So the electrical network is equivalent to AND gate that is option A.

Note:
Students DeMorgan’s first theorem and the second theorem are different from the DeMorgan’s first theorem we get $\overline{A.B}=\overline{A}+\overline{B}$ from DeMorgan’s second theorem we get $\overline{A+B}=\overline{A}.\overline{B}$ these two theorems will help to solve any electrical network with logic gates. NOR gate is equivalent to bubbled AND gate.