Truth-table sizing How many distinct input combinations appear in the truth table of a six-input AND gate?

Introduction / Context:Truth tables enumerate all possible input states. Estimating their size is essential for exhaustive testing, simulation, and Karnaugh map construction.

Given Data / Assumptions:

• Gate type: AND.
• Number of inputs: n = 6.
• Each input can be 0 or 1 (binary logic).

Concept / Approach:For n binary inputs, the total number of unique input combinations is 2^n. This is independent of the specific logic function (AND, OR, etc.).

Step-by-Step Solution:Compute 2^n with n = 6.2^6 = 64.Therefore, the truth table contains 64 rows (combinations).

Verification / Alternative check:List smaller cases: 2 inputs → 4 rows; 3 inputs → 8 rows; 4 inputs → 16 rows. Pattern doubles with each additional input, confirming 6 → 64.

Why Other Options Are Wrong:32: corresponds to 5 inputs (2^5).48 and 128: do not equal 2^n for integer n = 6.

Common Pitfalls:Confusing the number of combinations with the number of 1s in the output column; for an AND gate there is only one HIGH case (all inputs HIGH), but the table still lists all 64 input patterns.

Final Answer:64