Question
how many bits are needed to represent the following
9 unique things
9 unique things
Answers
GPT-4o mini
To determine how many bits are needed to represent 9 unique items, you can use the formula for the number of items that can be represented by \( n \) bits, which is \( 2^n \).
You need to find the smallest \( n \) such that \( 2^n \) is greater than or equal to 9.
Let's calculate:
- \( 2^3 = 8 \) (not enough)
- \( 2^4 = 16 \) (sufficient)
Since \( 2^4 = 16 \) is the first power of 2 that is greater than or equal to 9, you will need 4 bits to represent 9 unique things.
You need to find the smallest \( n \) such that \( 2^n \) is greater than or equal to 9.
Let's calculate:
- \( 2^3 = 8 \) (not enough)
- \( 2^4 = 16 \) (sufficient)
Since \( 2^4 = 16 \) is the first power of 2 that is greater than or equal to 9, you will need 4 bits to represent 9 unique things.