For a truth table with n binary inputs, the number of distinct input words (rows) is equal to which expression?

Introduction / Context:Truth tables enumerate all possible input combinations to fully define a combinational logic function. The size of the table grows exponentially with the number of inputs. Knowing the exact count of input words helps in planning testing, verification, and simplification steps like Karnaugh maps.

Given Data / Assumptions:

• There are n independent binary inputs.
• Each input can be either 0 or 1.
• Inputs are considered simultaneously to form input words (vectors).

Concept / Approach:Each binary input doubles the number of possible combinations. With one input, there are 2 possibilities. Adding a second input multiplies possibilities by 2 again, yielding 4. In general, with n independent binary inputs, the number of unique input words is 2^n. This exponential growth explains why exhaustive testing becomes infeasible for large n and why formal methods or random testing are used.

Step-by-Step Solution:Start with 1 input: combinations = 2.Add inputs one by one: each new input multiplies combinations by 2.After n inputs: combinations = 2 * 2 * … (n times) = 2^n.Select option “2^n.”

Verification / Alternative check:For n = 3, list inputs (A, B, C): there are 8 rows (000 through 111), which equals 2^3. For n = 4, there are 16 rows, consistent with 2^4.

Why Other Options Are Wrong:10^n corresponds to decimal digits, not binary choices; 4^n and 8^n would be correct only if each input had 4 or 8 states, which is not the case for binary inputs; “None” is false because 2^n is correct.

Common Pitfalls:Misreading 2^n as 2*n; forgetting that binary inputs are independent; overlooking that outputs do not affect the count of input rows—only inputs do.

Final Answer:2^n