Bits and Bytes: Understanding the Fundamentals of Binary Representation

[courtrigrad]

Hello everyone

I am enrolled in a AP Computer Science course. Currently we are learning about bits and bytes. Could someone please explain the concept of bits and bytes. For example, here are some questions that I have tried doing:

1. 16-bit binary numbers can be used to represent all non-negative integers from 0 to 2^16 - . I know that is is true, but why?

2. Design a method for representing the state of a tic-tac-toe board in computer memory. Can you fit your representation in three bytes?


I know that a tic-tav-toe board has 9 squares. However I become stuck after this.


Any help would greatly be appreciated.

Thanks

 

[Hurkyl]

1. 16-bit binary numbers can be used to represent all non-negative integers from 0 to 2^16 - . I know that is is true, but why?

It's also true that 16-digit decimal numbers can be used to represent all integers in the range [0, 10^16). Can you explain why?

2. Design a method for representing the state of a tic-tac-toe board in computer memory. Can you fit your representation in three bytes?

Have you tried anything at all?

 

[Tom McCurdy]

16 bits
2^0
2^1
2^2
2^3
2^4
2^5
2^6
2^7
2^8
2^9
2^10
2^11
2^12
2^13
2^14
2^15
2^16

think about this
this should give you the answer to number one