A Useful Property For The Powers Of 2
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.
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
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