Powers of 2 are very helpful in calculations. Candidates
should memorise powers of 2 upto 12 so that it can be used in the
questions.
20
1
21
2
22
4
23
8
24
16
25
32
26
64
27
128
28
256
29
512
210
1024
211
2048
212
4096
The sum of powers of 2 from 0 to any number n will be equal to 2n+1 – 1.
If a number is written from 1 to N as a sum of one or more of the
integers of a given set of integers, then it can easily be done from
powers of 2. The set of integers used by us comprise of all the powers
of 2 starting form 1 (i.e. 20) to the largest power of 2 less than or equal to N.
For example:
If you want to build all the integers
upto 255, the numbers 1, 2, 4, 8, 16, 32, 64, 128 are sufficient as
255=1+2+4+8+16+32+64+128.
Differently, if we have one weight each of 1, 2, 4, 8, 16, 32, 64
and 128 kg, then all the items would be measured from 1 kg to 255 kg
using one or more of the given weights (the weights used only in one pan
of the weighing scales).
Example:
How much minimum number of weights are
required to weigh all possible weights upto 512 Kg (Putting all the
weights only in one side of pan)
Solution:
512=29. Minimum Number of weights required=9+1=10. The weights will be 1,2, 4, 8, 16, 32, 64,128, 256 kg
