Question
how many bits are needed to represent the following
h.150 unique things
h.150 unique things
Answers
GPT-4o mini
To determine how many bits are needed to represent 150 unique items, you can use the formula that relates the number of bits (\(n\)) to the number of unique values (\(N\)):
\[
N = 2^n
\]
To find the smallest \(n\) such that \(2^n \geq 150\), you can calculate the powers of 2:
- \(2^7 = 128\)
- \(2^8 = 256\)
Since \(128 < 150 < 256\), you need at least \(n = 8\) bits to represent 150 unique things.
Therefore, **8 bits** are needed to represent the 150 unique items.
\[
N = 2^n
\]
To find the smallest \(n\) such that \(2^n \geq 150\), you can calculate the powers of 2:
- \(2^7 = 128\)
- \(2^8 = 256\)
Since \(128 < 150 < 256\), you need at least \(n = 8\) bits to represent 150 unique things.
Therefore, **8 bits** are needed to represent the 150 unique items.