Question

A computer uses ternary system instead of the traditional binary system. An n bit string in the binary system will occupy
1. 3 + n ternary digits
2. 2n/3 ternary digits
3. n(log₂3) ternary digits
4. n(log₃2) ternary digits

Answer 1

Correct Answer - Option 4 : n(log₃2) ternary digits

Concept:

Maximum number possible using n-bit in Binary: 2ⁿ – 1

Maximum number possible using x bit in Ternary: 3^x – 1

Both will take different numbers of bits to represent the same number.

Explanation

3^x – 1 = 2ⁿ – 1

3^x = 2ⁿ

Taking log₃ on both side

log₂ (3x)= log2 (2n)

x.log3 (3) = n × log3 (2 )

x =  n × log3 (2 )