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Normalization

Represents the normalized representation of floating point numbers
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Normalization is also called Normalized number , is a representation Floating point number Can also be modified by Order code And move at the same time Mantissa To make it meet this specification.
Chinese name
Normalization
Foreign name
specification
Alias
Normalized number
Meaning
Denotes the normalized representation of floating point numbers
Characteristics
Floating point numbers are approximate

Basic concepts

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The normalized floating point number is called Normalized number stay Floating point number In order to represent the most valid Data bits At the same time, the floating point number has a fixed representation. The floating point number should be encoded in a certain standard, and the mantissa part should be pure decimal Given and mantissal absolute value It should be greater than or equal to 1/R and less than or equal to 1, that is decimal point The first digit after is not zero. The specification of this representation is called the normalized representation of floating point numbers. Data that do not meet this requirement can be modified by Order code The method of moving the mantissa at the same time makes it meet this specification.

Main characteristics

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Floating point number Normalized form of:
Floating point numbers are all Approximate representation The precision is determined by the mantissa, and the size of the number representation range is determined by R and E. In order to improve accuracy, it is necessary to Significant digits Take up as many available bits as possible. This measure is called the normalization of floating point numbers. Tailor of normalization requirements:
When R=2,
The process of converting a floating point number to normalization is called floating point number normalization.
Right gauge: move the mantissa one position to the right, Order code +1
Left gauge: mantissa Shift Left One digit, order code - 1

Implementation method

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Note: Hidden position
about Normalized floating point number The first value after the decimal point is fixed( Positive number : 1, negative: Original code 1, Complement 0), so this bit is often defaulted and is called the hidden bit.

Normalized format of different codes

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Positive number: original code is 0.1xxxxxx, complement code is 0.1xxxxxxxx
Negative number: original code is 1.1xxxxxx, complement code is 1.0xxxxxxxx