It is important for a Computer Scientist to know the p= owers 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 |

0 |
1 |

1 |
2 |

2 |
4 |

3 |
8 |

4 |
16 |

5 |
32 |

6 |
64 |

7 |
128 |

8 |
256 |

9 |
512 |

10 |
1024 |

11 |
2048 |

12 |
4096 |

20 |
1048576 |

30 |
1073741824<= /p> |

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 =3D number of bits

T =3D B / 10 &nbs=
p; &=
nbsp; integer
division =
*(**first decimal digits)*

R =3D B mod 10 &n=
bsp; remainder
of above division *(last decimal dig=
it)*

Using the above table get M =3D 2^{R}

Decimal value is M * 10^{3T}

For example: DES keys are 5= 6 bits in length. How many possible = key values are there?

T =3D 5 &nb= sp; R =3D 6 M =3D 64

There are approximately 64 * 10^{15} possible =
key
combinations.