How many possible input combinations are there for a logic gate with 3 inputs?

Question

BlackTom AI · Accepted Answer

Let's unpack what the question is asking. It concerns the number of input combinations for a logic gate that has 3 inputs, meaning each input bit can be either 0 or 1.
Option a: 4. This would correspond to having only 2 inputs (2^2 = 4), or to some constrained subset of cases, but with 3 inputs the total combinations grow beyond 4, so this is not correct.
Option b: 16. This would be the result of 2^4, i.e., if there were 4 inputs. Since we have 3 inputs, 4 is not the right base count for the exponent.
Option c: 8. The total number of input combinations for n inputs is 2^n. Here n = 3, so 2^3 = 8, which matches the expected count of all possible 0/1 patterns across the three inputs.
Option d: 2. This would correspond to a single input bit, or perhaps a scenario with extreme restriction, but with three inputs there are far more combinations than two.
In summary, the correct way to count is to use powers of two for each independent input bit, multiplying possibilities (0 or 1) across all three inputs, yielding 2 × 2 × 2 = 8. The options presented align as 4 (too small), 16 (too large, corresponding to four inputs), 8 (matches the correct calculation), and 2 (too small for three inputs).}

System Software and Computing Concepts (102025-ABB) Tutorial 3: Digital Logic Circuits

How many possible input combinations are there for a logic gate with 3 inputs?

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