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How many bits are require to represent an arbitrary number X?

(assume unsigned number). I get that to represent 5 states, you need 3 bits (b/c you can represent 8 total with 3 bits). But when you represent a certain number like 5,435, how do you find out the number of bits needed? How many bits are then required to represent an arbitrary number X?

Public Comments

1. Well..... bits really are just the computer's way of storing the binary data. So whatever number you have, convert it to binary, and the number of 1/0s are how many bits would be needed. In your example, 5 in binary is 101, thus the 3 bits. And a byte is 8 bits because every character in ASCII can be represented using just an 8 digit binary number.
2. 5435 is base 10. Write it in binary, count the digits! Not very practical for "arbitrary number", unless you write a program to do so... That program will just convert base 10 in base 2. You could, also, make a table of "limits" 1 bit, 0 and 1, max = 1 (2-1) 2 bits, max = 3 (4-1) 3 bits, max = 7 (8-1) 4 bits, max = 15 (16-1) 5 bits, max = ... 8 bits: 255 16 bits: 65535 etc... check in which range the "arbitrary number" fits...
3. Number of bits N = log (base 2) X, rounded up to the nearest integer.