## The Binary (Base-2) System

Binary, by definition, is the base-2 system. This means that each column can contain any number up to, but not including, 2. Hence only 0 and 1 are permissible in any column.

Consider the example binary number: 10001011*B*.

(Note the use of the B at the end of the number, used by convention
to define the base system being used, namely binary.) In each column, there
is either one of that column's value (1) or not (0). The rightmost column in the
number above is (as with the decimal system), the units column. This
is because 2 raised to the power of 0 is 1. The next column along is
the number of 'twos' present (since 2 raised to the power of 1
is 2). The third column from the right is the 'fours'
column (2^{2} = 2 x 2 = 4).
The fourth column holds the number of 'eights' (since 2 x 2 x 2 = 8).
This continues as indicated in the table below. So the binary
number above can be decomposed (starting from the right) as follows:

(1 x 1) + (1 x 2) + (0 x 4) + (1 x 8) + (0 x 16) + (0 x 32) + (0 x 64) + (1 x 128) = 139.

128s (2 ^{7}) |
64s (2 ^{6}) |
32s (2 ^{5}) |
16s (2 ^{4}) |
8s (2 ^{3}) |
4s (2 ^{2}) |
2s (2 ^{1}) |
Units (2 ^{0}) |
---|---|---|---|---|---|---|---|

1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 |

128 | 0 | 0 | 0 | 8 | 0 | 2 | 1 |

That's binary in a nutshell. Simple, innit?

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 |

Now let's take a look at bits and bytes and various other scraps of IT quantitative terminology.

Just Too Good Last updated: June, 2006 (DJL) |