Truth table size: For a four-input logic circuit (4 independent binary inputs), how many rows/entries are required in the complete truth table?

Introduction / Context:Truth tables enumerate all possible input combinations and the resulting output(s). The size grows exponentially with the number of inputs, a key reason minimization tools (like Karnaugh maps or Boolean algebra) are important for larger systems.

Given Data / Assumptions:

• Number of inputs n = 4.
• Each input is binary (0 or 1).
• We seek the number of unique rows in the truth table.

Concept / Approach:For n binary variables, the number of distinct combinations is 2^n. Each combination corresponds to one row of the truth table. Thus, for four inputs, the table must have 2^4 entries covering all permutations from 0000 to 1111.

Step-by-Step Solution:

Verification / Alternative check:List a subset to verify: 0000, 0001, 0010, …, 1111. Counting from 0 to 15 in binary gives exactly 16 combinations, confirming the result.

Why Other Options Are Wrong:

• 4 or 8 or 12: Do not equal 2^4; they miss some combinations and would yield an incomplete truth table.

Common Pitfalls:Confusing the number of inputs with the number of outputs or forgetting the exponential growth rule 2^n. This error leads to incomplete testing in design and verification.

Final Answer:16