Question
how many bits are needed to represent the following
i. 550 unique things
i. 550 unique things
Answers
GPT-4o mini
To determine how many bits are needed to represent a certain number of unique items, you can use the formula for calculating the number of bits required to represent a number of distinct values:
\[
n = 2^b
\]
where \( n \) is the number of unique items and \( b \) is the number of bits.
For your case, you want to find the smallest \( b \) such that \( 2^b \geq 550 \).
Let's calculate it:
1. Start by calculating the powers of 2:
- \( 2^8 = 256 \) (not sufficient)
- \( 2^9 = 512 \) (still not sufficient)
- \( 2^{10} = 1024 \) (sufficient)
So, \( 2^{10} = 1024 \) is the first power of 2 that is greater than or equal to 550.
Thus, you need **10 bits** to represent 550 unique things.
\[
n = 2^b
\]
where \( n \) is the number of unique items and \( b \) is the number of bits.
For your case, you want to find the smallest \( b \) such that \( 2^b \geq 550 \).
Let's calculate it:
1. Start by calculating the powers of 2:
- \( 2^8 = 256 \) (not sufficient)
- \( 2^9 = 512 \) (still not sufficient)
- \( 2^{10} = 1024 \) (sufficient)
So, \( 2^{10} = 1024 \) is the first power of 2 that is greater than or equal to 550.
Thus, you need **10 bits** to represent 550 unique things.