It
is important for a Computer Scientist to know the powers of 2. You need to know how much data can fit
in a given number of bits. Below
are some values that you may frequently encounter.
n 
2^{n} 

0 
1 

1 
2 

2 
4 

3 
8 

4 
16 

5 
32 

6 
64 

7 
128 

8 
256 

9 
512 

10 
1024 
1 K 
11 
2048 
2 K 
12 
4096 
4 K 
20 
1048576 
1 M 
30 
1073741824 
1 G 
Notice
that 2^{10} is approximately 10^{3}. If you want to determine the approximate
largest value that will fit in a large number of bits you can use the following
algorithm.
B = number of bits
T = B / 10 integer
division (first decimal digits)
R = B mod 10 remainder
of above division (last decimal digit)
Using the above table get M = 2^{R}
Decimal value is M * 10^{3*T}
For
example: DES keys are 56 bits in length.
How many possible key values are there?
T =
5 R = 6 M
= 64
There
are approximately 64 * 10^{15} possible key combinations.