Question
how many bits are needed to represent the following
b.137 unique things
b.137 unique things
Answers
GPT-4o mini
To determine how many bits are needed to represent 137 unique items, we can use the formula:
\[
\text{Bits needed} = \lceil \log_2(n) \rceil
\]
where \( n \) is the number of unique items, and \( \lceil x \rceil \) represents the ceiling function, which rounds \( x \) up to the nearest whole number.
Now, we can calculate \( \log_2(137) \):
\[
\log_2(137) \approx 7.13
\]
Taking the ceiling of this value:
\[
\lceil 7.13 \rceil = 8
\]
Therefore, **8 bits** are needed to represent 137 unique things.
\[
\text{Bits needed} = \lceil \log_2(n) \rceil
\]
where \( n \) is the number of unique items, and \( \lceil x \rceil \) represents the ceiling function, which rounds \( x \) up to the nearest whole number.
Now, we can calculate \( \log_2(137) \):
\[
\log_2(137) \approx 7.13
\]
Taking the ceiling of this value:
\[
\lceil 7.13 \rceil = 8
\]
Therefore, **8 bits** are needed to represent 137 unique things.