Imagine we wanted to create a system that would allow you to represent each of the 50 states. what's the smallest number of bits you would need to ensure you'd have unique patterns for each state? write down how you would represent these 3 different states in your system. then add two more of your own. ex: wyoming arizona vermont wyoming arizona vermont nevada me

To represent 50 different 'things' (e.g., states), you need 2log50 = 6 bits.

With 1 bit you can represent 2 things, with 2 bits 4 things, with 3 bits 8 things and so forth (it doubles everytime). 5 bits is not enough because then you're at 32, but 6 bits suffices because you then have 2^6 = 64 possibilities.

Your numbering could start at 000000=Wyoming, 000001=Arizona, 000010=Vermont. The numbering continues like 000011, 000100, 000101, etc. all the way up to 111111, that's the last number.