One approach to handling fuzzy logic data might be to design a computer using…
2007
One approach to handling fuzzy logic data might be to design a computer using ternary (base-3) logic so that data could be stored as "true," "false," and "unknown." If each ternary logic element is called a flit, how many flits are required to represent at least 256 different values?
Answer: C. 6 — ConceptIn a positional number system with base b, each digit can take b values. Therefore, n independent base-b digits can represent bn distinct patterns. To…
- A.
4
- B.
5
- C.
6
- D.
7
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Correct answer: C
Concept
In a positional number system with base b, each digit can take b values. Therefore, n independent base-b digits can represent bn distinct patterns. To represent at least N values, choose the smallest integer n for which bn ≥ N.
Application
Here the base is 3, so n flits can represent 3n patterns.
For 5 flits, 35 = 243, which is less than 256; therefore 5 flits are insufficient.
For 6 flits, 36 = 729, which is at least 256; therefore 6 flits meet the requirement.
Cross-check
The minimum must lie between two consecutive powers of 3. Because 243 < 256 ≤ 729, the least valid exponent is 6.
Result
At least 6 flits are required.