Question

how many bits are needed to represent the following
g.87 unique things

Answer 1

To determine how many bits are needed to represent a certain number of unique things, you can use the formula for calculating the number of bits required to uniquely identify \( n \) items, which is:

\[
\text{bits} = \lceil \log_2(n) \rceil
\]

where \( \lceil x \rceil \) denotes the ceiling function, which rounds \( x \) up to the nearest integer, and \( \log_2 \) is the logarithm base 2.

For 87 unique things, we need to compute:

\[
\log_2(87)
\]

Using a calculator to find \( \log_2(87) \):

\[
\log_2(87) \approx 6.075
\]

Now, applying the ceiling function:

\[
\lceil 6.075 \rceil = 7
\]

So, you need **7 bits** to represent 87 unique things.