Normalization

Some numbers can have 2 or more different representations.

Example: The number $36_{10}$ from the previous example can be represented by

+---+   +---+---+---+---+---+   +---+---+---+---+---+
| 0 |   | 1 | 0 | 1 | 0 | 1 |   | 1 | 0 | 0 | 1 | 0 | = 0.10010 x 2^6 = 36_{10}
+---+   +---+---+---+---+---+   +---+---+---+---+---+

or, equivalently, by

+---+   +---+---+---+---+---+   +---+---+---+---+---+
| 0 |   | 1 | 0 | 1 | 1 | 0 |   | 0 | 1 | 0 | 0 | 1 | = 0.01001 x 2^7 = 36_{10}
+---+   +---+---+---+---+---+   +---+---+---+---+---+

The representation in which the leftmost bit of the significand is $1$ is called the normalized form. The process of expressing a given number in its normalized form is called normalization. In our example, $0.10010 \times 2^6$ is the normalized form of $36_{10}$.