Decoder sizing — number of outputs for a 6-bit binary input If a binary decoder accepts a 6-bit input (values 0–63), how many distinct output lines are available in a fully decoded one-of-N arrangement?
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A16
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B32
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C64
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D128
Answer
Correct Answer: 64
Explanation
Introduction / Context:Binary decoders map an n-bit input to one-of-2^n outputs, activating exactly one output for each input code. Properly sizing decoders is fundamental when designing address decoders, channel selectors, and state decoders.
Given Data / Assumptions:
- Number of input bits n = 6.
- Fully decoded, one-hot output behavior.
- No invalid codes because all 6-bit combinations are valid (0–63).
Concept / Approach:The number of outputs in a full binary decoder equals 2^n. With n = 6, 2^6 = 64 outputs. Each output corresponds to one unique input value; only that line is asserted at any given time.
Step-by-Step Solution:
Compute 2^n for n = 6 → 2^6 = 64.Interpretation: one output per input code (0–63).Therefore, total outputs = 64.Verification / Alternative check:Compare with common decoder families: 3-to-8 (2^3), 4-to-16 (2^4). Extending the pattern to 6 bits yields 64 outputs.
Why Other Options Are Wrong:
- 16 and 32 correspond to 4-bit and 5-bit decoders.
- 128 corresponds to 7-bit decoding.
Common Pitfalls:Confusing a BCD-to-decimal decoder (10 outputs) with a full binary decoder (2^n outputs).
Final Answer:64