4-bit counter capacity — maximum modulus A binary counter built from 4 flip-flops has what maximum modulus (number of unique states before repeating)?

Introduction / Context:
The number of flip-flops determines the maximum count range of a binary counter. Each flip-flop adds one binary digit, doubling the number of available states and thereby increasing the modulus by a factor of two. This is a fundamental design relationship in digital electronics.

Given Data / Assumptions:

• Counter uses 4 flip-flops.
• Binary counting (no skipped states), starting from 0000.

Concept / Approach:
An n-bit binary counter can represent 2^n distinct states. For n = 4, the number of states is 2^4 = 16, typically ranging from 0 to 15 in unsigned representation. Unless additional logic truncates the sequence, the natural modulus equals 16.

Step-by-Step Solution:

Verification / Alternative check:
Enumerate outputs from 0000 to 1111. Counting the number of unique 4-bit patterns yields 16, after which the counter repeats at 0000.

Why Other Options Are Wrong:

• 3, 6, 8: correspond to other moduli (e.g., MOD-8 uses 3 flip-flops).
• 32: requires 5 flip-flops (2^5).

Common Pitfalls:

• Confusing modulus with maximum count value; modulus is the number of states (0–15 inclusive gives 16 states).

Final Answer:
16