**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.2^{0} | 1 |

2^{1} | 2 |

2^{2} | 4 |

2^{3} | 8 |

2^{4} | 16 |

2^{5} | 32 |

2^{6} | 64 |

2^{7} | 128 |

2^{8} | 256 |

2^{9} | 512 |

2^{10} | 1024 |

2^{11} | 2048 |

2^{12} | 4096 |

- The sum of powers of 2 from 0 to any number n will be equal to 2
^{n+1}– 1.

^{0}) 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=2

^{9}. Minimum Number of weights required=9+1=10. The weights will be 1,2, 4, 8, 16, 32, 64,128, 256 kg