Combinatorics of truth tables: an AND gate has 7 inputs. How many distinct input words (rows) appear in its complete truth table?

Introduction / Context:
Truth tables enumerate all possible input combinations for a logic function. For n binary inputs, there are 2^n combinations. This question checks the ability to compute the size of the truth table for a 7-input logic gate (AND, but the count depends only on n).

Given Data / Assumptions:

• Number of inputs n = 7.
• Each input is binary (0 or 1).
• Truth table includes all unique input combinations.

Concept / Approach:
The count of binary words of length n is 2^n. Thus, for n = 7, we have 2^7 total rows. This is independent of the logic function; AND, OR, XOR etc. share the same number of rows for the same n.

Step-by-Step Solution:

Verification / Alternative check:
List sizes grow as 2, 4, 8, 16, 32, 64, 128 for n = 1…7, confirming 128 for n = 7.

Why Other Options Are Wrong:

Common Pitfalls:
Using 2*n instead of 2^n; confusing number of outputs with number of table rows.

Final Answer:
128