How to find the length of a number in bits?

Question

Programming

Can you please explain what is the "length of a number in bits", what should be done to determine it?
Let's say Wikipedia says that I need to take a number of 1024 bits, and below is an example, and there is a number, only it seems to me that they have it less.
Please tell us how it works?

Answer 1

how is it "the length of the number in bits", what should be done to determine it.

This is the number of bits required to write the number.
You need to take the next larger integer after the base 2 logarithm of the number. 1 -- 1 bit, 2 -- 2 bits, 3 -- 2 bits, 4 -- 3 bits... 1023 -- 10 bits, 1024 -- 11 bits... ) -- 1024 bits, 179,769,313,486,231,590,772,930,...,304,835,356,329,624,224,137,216 -- 1025 bits...

Answer 2

To determine how many bits you need at least to store a number, you need to take its logarithm to base 2 (you first need to add 1, because we also take into account 0). If the result is not an integer (the number is not a power of 2), then it is worth rounding it up:
log2(255 + 1) = 8 - then the number will fit into 8 bits
log2(256 + 1) = 8.0056... - round up to 9
This scheme does not work for 0. You need to remember that it also needs one bit :)

Answer 3

128 byte integer?