Q.44 Truth table of a logic gate is given below:

The value of X in the above table is __________.

The value of X in the given truth table is 1, and the logic gate is a NAND gate.​

Question recap

The question provides a truth table of a logic gate:

Task: Identify the logic gate and compute the unknown output X.

Step‑by‑step solution

1. Recall standard truth tables

   • AND gate gives output 1 only when both inputs are 1.​

   • OR gate gives output 1 when at least one input is 1.​

   • NAND gate is the negation of AND, so it gives output 0 only when both inputs are 1, and 1 otherwise.​

   • NOR gate is the negation of OR, so it gives output 1 only when both inputs are 0.​

2. Compare the first three rows

   • For inputs $A=0,B=0$, output is 1.

     • This matches NAND (1) and NOR (1), but does not match AND (0) or OR (0).​

   • For inputs $A=0,B=1$, output is 1.

     • This matches OR (1) and NAND (1), but not AND (0) or NOR (0).​

   • For inputs $A=1,B=1$, output is 0.

     • This matches AND (1 → no), OR (1 → no), NOR (0 → yes), NAND (0 → yes).​

   A gate whose truth table (for the three known rows) is 1,1,0 must be either NAND or NOR.

3. Use logical reasoning to choose between NAND and NOR

   • NOR gate outputs 0 whenever any input is 1.​

     • So for $A=0,B=1$, NOR must give 0, but the table shows 1, so NOR is impossible.

   • NAND gate outputs 1 except when both inputs are 1.​

     • For $A=0,B=1$, NAND gives 1, which matches the table.
       Therefore the only consistent gate is NAND.

4. Determine X using the NAND rule

   • NAND output: Y=A⋅B‾Y=A⋅B.​

   • For the last row, $A=1$ and $B=0$:

     • $A\cdot B=1\times 0=0$.

     • Y=0‾=1Y=0=1.

   • Hence, the missing value X = 1.

So the completed truth table is:

Explanation of common gate options

If the MCQ listed basic gates, the reasoning for each would be:

• AND gate

  • Truth table: outputs 1 only for 1,1 and 0 for all other combinations.​

  • Given table has 1 for 0,0 and 0,1, so it cannot be AND.

• OR gate

  • Truth table: 0,0 → 0; 0,1 → 1; 1,0 → 1; 1,1 → 1.​

  • Given table has 0,0 → 1 and 1,1 → 0, so it cannot be OR.

• NOR gate

  • Truth table: 0,0 → 1; 0,1 → 0; 1,0 → 0; 1,1 → 0.​

  • Given table requires 0,1 → 1, so NOR is ruled out.

• NAND gate

  • Truth table: 0,0 → 1; 0,1 → 1; 1,0 → 1; 1,1 → 0.​

  • This exactly matches all rows if X is taken as 1, so the logic gate is NAND and X = 1.

SEO‑friendly introduction using key phrase

The truth table of a logic gate NAND gate is a fundamental concept in digital electronics and competitive exams like CSIR NET and GATE. By analysing how a NAND gate responds to every possible combination of inputs A and B, students can easily find missing outputs such as the unknown value X in a given truth table.​