Question
how many bits are needed to represent the following
a.52 unique things:
a.52 unique things:
Answers
GPT-4o mini
To determine how many bits are needed to represent 52 unique things, you can use the formula for the number of unique combinations that can be represented with \( n \) bits, which is \( 2^n \).
You need to find the smallest \( n \) such that:
\[
2^n \geq 52
\]
Calculating the powers of 2:
- \( 2^5 = 32 \) (not enough)
- \( 2^6 = 64 \) (sufficient)
Since \( 2^6 = 64 \) is the smallest power of 2 that is greater than or equal to 52, you need **6 bits** to represent 52 unique things.
You need to find the smallest \( n \) such that:
\[
2^n \geq 52
\]
Calculating the powers of 2:
- \( 2^5 = 32 \) (not enough)
- \( 2^6 = 64 \) (sufficient)
Since \( 2^6 = 64 \) is the smallest power of 2 that is greater than or equal to 52, you need **6 bits** to represent 52 unique things.