The 36 characters made up of the 26 capital letters and the 10 digits are to be distinguished by bit strings all of the same length (a fixed-length code). Which of the following is the minimum number of bits needed per character?

Answer: B. 6 bits

n bits can distinguish 2ⁿ cases, so we need the smallest n with 2ⁿ ≥ 36. 2⁵ = 32 is not enough and 2⁶ = 64 is, so the answer is 6 bits. It is also log₂ 36 ≈ 5.17 rounded up to a whole number.

• A. 5 bits can distinguish only 2⁵ = 32 cases, too few for 36 characters.
• B. Correct. 2⁶ = 64 ≥ 36.
• C. 36 bits is the case where each character gets its own bit and exactly one bit is 1 (one-hot), which is not the minimum.