Designing a MOD-32 binary counter — number of flip-flops How many flip-flops are required to construct a MOD-32 binary counter (i.e., a counter that cycles through 32 distinct states)?
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A3
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B45
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C5
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D6
Answer
Correct Answer: 5
Explanation
Introduction / Context:Binary counters implemented with flip-flops have a number of states equal to 2^n, where n is the number of flip-flops (bits). Determining the number of flip-flops needed for a target modulus is a foundational skill for digital timing and sequencing design.
Given Data / Assumptions:
- We need a counter with 32 distinct states (MOD-32).
- Each flip-flop contributes one binary digit (bit).
- States grow as powers of two: 2^n.
Concept / Approach:Find the smallest n such that 2^n ≥ 32. Because 2^5 = 32, five flip-flops are exactly sufficient and produce the required modulus without wasted states.
Step-by-Step Solution:
1) Evaluate powers: 2^4 = 16 (insufficient).2) Next power: 2^5 = 32 (matches requirement).3) Therefore, n = 5 flip-flops.4) Implement as ripple or synchronous as needed for timing constraints.Verification / Alternative check:Simulate a 5-bit counter; it cycles through 00000 to 11111 (32 states) before repeating.
Why Other Options Are Wrong:
- 3 and 6 do not yield 32 states (2^3=8, 2^6=64).
- 45 is unrelated and not a number of flip-flops.
Common Pitfalls:Confusing decimal modulus with binary powers; forgetting that extra states appear if n is larger than necessary.
Final Answer:5