calculation of bits needed

Question

I need help with this

I was asked that for an unsigned integer range 1 to 1 billion, ,how many bits are needed!

How do we calculate this?

Thank you

UPDATE!!!!

This what I wanted to know because the interviwer said 17

What part of base 2 confuses you? Could you be more specific on what you can't figure out? — S.Lott, Nov 19 '10 at 19:36
If your interviewer said 17 then he's either just plain wrong, or you aren't giving us the whole question. — Peter Alexander, Nov 19 '10 at 19:38
Either your interviewer is an idiot, or you've mis-stated the question. 17 bits will get you any number from 0 to 131071. If you start at 1, you can represent numbers up to 131072. — nmichaels, Nov 19 '10 at 19:40
The interviewer must have confused between 1 lakh and 1 billion. — Manoj R, Nov 22 '10 at 06:05
And if your calculator doesn't have log_2 built in, you can exploit that log_b(x) = log_k(x)/log_k(b) (i.e. log_2(1e9) = log(1e9)/log(2)). — , Nov 19 '10 at 19:38

score 7 · Answer 1 · answered Nov 19 '10 at 19:35

Take the log base 2 of 1 billion and round up.

Alternatively, you should know that integers (with over 4 billion values) require 32-bits, therefore for 2 billion you'd need 31-bits and for 1 billion, 30-bits.

Another handy thing to know is that every 10 bits increase the number of values you can represent by a factor just over 1000 (1024), so for 1000, you need 10 bits, 1 million needs 20 bits, and 1 billion needs 30 bits.

score 3 · Accepted Answer · answered Nov 19 '10 at 19:34

3

Calculate log2(1000000000) and round it up. It works out to 30 bits.

For example in Python you can calculate it like this:

>>> import math
>>> math.ceil(math.log(1000000000, 2))
30.0

answered Nov 19 '10 at 19:34

Mark Byers

811,555
193
1,581
1,452

score 2 · Answer 3 · answered Nov 19 '10 at 19:37

2

2^10 = 1024
2^10 * 2^10 = 2^20 = 1024*1024 = 1048576
2^10 * 2^10 * 2^10 = 2^30 = 3 * 1024 ~= 1,000,000

=> 30 Bits

answered Nov 19 '10 at 19:37

KingCrunch

128,817
21
151
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calculation of bits needed

3 Answers3