A computer uses ternary system instead of the traditional binary system. An n…
2018
A computer uses ternary system instead of the traditional binary system. An n bit string in the binary system will occupy
- A.
3 + n ternary digits
- B.
2n / 3 ternary digits
- C.
n(log23) ternary digits
- D.
n(log32 ) ternary digits
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Correct answer: D
To determine the equivalent number of ternary digits for an n-bit binary string, we compare the total distinct values each system can represent.
An n-bit binary string represents 2^n distinct values. An m-digit ternary string represents 3^m distinct values.
Equating these gives 2^n = 3^m. Solving for m using logarithms yields m = n * log_3(2). Therefore, an n-bit binary string occupies approximately 0.631n ternary digits.
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