MCQEasyJEE 2023Logic Gates

JEE Physics 2023 Question with Solution

For the given logic gates combination, the correct truth table will be:

Logic gate circuit with inputs A and B, each passing through a NOT gate and combined through two AND gates whose outputs go to an OR gate producing output X.
  • A
    Truth table with columns A, B, X showing rows 0 0 1; 0 1 0; 1 0 0; 1 1 0.
  • B
    Truth table with columns A, B, X showing rows 0 0 0; 0 1 1; 1 0 1; 1 1 0.
  • C
    Truth table with columns A, B, X showing rows 0 0 1; 0 1 0; 1 0 1; 1 1 0.
  • D
    Truth table with columns A, B, X showing rows 0 0 0; 0 1 1; 1 0 1; 1 1 1.

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: A combination of NOT, AND, and OR gates is shown. Find: Which truth table gives the correct output XX.

The solution states that the inputs AA and BB are first inverted by the NOT gates, then combined through AND gates, and finally passed through the OR gate.

From the extracted truth table analysis:

  • When A=0A = 0 and B=0B = 0, X=1X = 1
  • When A=0A = 0 and B=1B = 1, X=0X = 0
  • When A=1A = 1 and B=0B = 0, X=1X = 1
  • When A=1A = 1 and B=1B = 1, X=0X = 0

So the required truth table is:

ABX001010101110\begin{array}{c c c} A & B & X \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}

This matches Table 3.

Therefore, the correct option is C.

Truth Table Comparison

Given: Four table options are provided as images. Find: Which one matches the output pattern stated in the solution.

Compare the rows one by one:

  1. For A=0A = 0, B=0B = 0, output must be 11.
  2. For A=0A = 0, B=1B = 1, output must be 00.
  3. For A=1A = 1, B=0B = 0, output must be 11.
  4. For A=1A = 1, B=1B = 1, output must be 00.

Among the given image options, only option C shows the sequence:

1,0,1,01, 0, 1, 0

for the rows

(0,0),(0,1),(1,0),(1,1)(0,0), (0,1), (1,0), (1,1)

respectively.

Hence, the correct option is C.

Common mistakes

  • A common mistake is to ignore the NOT gates and read the circuit as a direct AND-OR combination. That changes the intermediate inputs and gives the wrong truth table. Always invert the relevant inputs first.

  • Students often compare only one or two rows of the truth table and stop early. This is wrong because a partially matching table may still fail in another input case. Check all four combinations of AA and BB.

  • Another mistake is to confuse the final gate as AND instead of OR. That changes how the two intermediate outputs combine. Identify each gate symbol carefully before writing the truth table.

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