Two 4 bits binary numbers, $$A = 1101$$ and $$B = 1010$$ are given in the inputs of a logic circuit shown in figure below . The output $$(Y)$$ will be :

A pair of cross-connected NAND gates (as drawn in the question) behaves exactly like a 2-input Exclusive-OR (XOR) gate. For two logic levels $$a$$ and $$b$$ the circuit gives the function

$$Y = a \oplus b = \bar a\,b + a\,\bar b$$

Because the same arrangement is repeated for every corresponding bit, the 4-bit output $$Y_3Y_2Y_1Y_0$$ is obtained by XOR-ing each bit of $$A$$ with the same-position bit of $$B$$.

Write the two numbers from the most-significant bit (MSB) to the least-significant bit (LSB):

$$A = A_3A_2A_1A_0 = 1\;1\;0\;1$$
$$B = B_3B_2B_1B_0 = 1\;0\;1\;0$$

Now evaluate the XOR bit by bit using the rule $$1\oplus1=0,\;1\oplus0=1,\;0\oplus1=1,\;0\oplus0=0$$.

Bit-wise computation

MSB $$Y_3 = 1 \oplus 1 = 0$$

Next $$Y_2 = 1 \oplus 0 = 1$$

Next $$Y_1 = 0 \oplus 1 = 1$$

LSB $$Y_0 = 1 \oplus 0 = 1$$

Collecting the four results gives

$$Y = Y_3Y_2Y_1Y_0 = 0\;1\;1\;1 = 0111$$

Hence the output of the circuit is

Option C which is: $$Y = 0111$$