Numerical coding

In the form of various numerical values ​​in a computer data representing the number of machines it referred to. The actual value of the number corresponding to the machine referred to the number of truth values.

Fixed-point and floating-point difference

Fixed point

Fixed decimal point

Float

F = M * 2E

M: Mantissa

E: exponent

Typically floating point numbers comprising: a numerical character part number, symbol order, numerical order code part, the mantissa

 

Original code

definition

(1) integer

\[\left[ X \right]{\rm{ =  }}\left\{ {\begin{array}{*{20}{c}}
{X{\rm{     }}({\rm{0}} \le X{\rm{  < }}{{\rm{2}}^{n - 1}}{\rm{)  }}}\\
{{2^{n - 1}} - X{\rm{     }}({\rm{ - }}{{\rm{2}}^{n - 1}}{\rm{  <  }}X \le 0){\rm{  }}}
\end{array}} \right.\]

In fact, represent the highest level in line with other bits represent the absolute value

(2) floating-point number

\[\left[ X \right]{\rm{ =  }}\left\{ {\begin{array}{*{20}{c}}
{X{\rm{     }}({\rm{0}} \le X{\rm{  <  1)  }}}\\
{{2^{n - 1}} - X{\rm{     }}({\rm{ - 1  <  }}X \le 0){\rm{  }}}
\end{array}} \right.\]

advantage

Simple and intuitive

Shortcoming

(1) addition and subtraction problems

(2) 0 means no unique

 

Complement

definition

(1) integer

\[\left[ X \right]{\rm{ =  }}\left\{ {\begin{array}{*{20}{c}}
{X{\rm{     }}({\rm{0}} \le X{\rm{  <  }}{{\rm{2}}^{n - 1}}{\rm{)  }}}\\
{{2^n} + X{\rm{     }}( - {2^{n - 1}}{\rm{ }} \le X < 0){\rm{  }}}
\end{array}(\bmod {2^n})} \right.\]

Complement negative number is the positive value indicates bitwise plus 1 

(2) floating-point number

\[\left[ X \right]{\rm{ =  }}\left\{ {\begin{array}{*{20}{c}}
{X{\rm{     }}({\rm{0}} \le X{\rm{  <  1)  }}}\\
{2 + X{\rm{     }}( - 1{\rm{ }} \le X < 0){\rm{  }}}
\end{array}(\bmod 2)} \right.\]

advantage

(1) represents a unique 0

(2) Most processors are provided complementary operations

(3) simple subtraction: [X + Y] Complement = [X] Complement + [Y] Complement

 

Inverted

definition

(1) integer

\[\left[ X \right]{\rm{ =  }}\left\{ {\begin{array}{*{20}{c}}
{X{\rm{     }}({\rm{0}} \le X{\rm{  <  }}{{\rm{2}}^{n - 1}}{\rm{)  }}}\\
{({2^n} - 1) + X{\rm{     }}( - {2^{n - 1}}{\rm{  <  }}X \le 0){\rm{  }}}
\end{array}(\bmod ({2^n} - 1))} \right.\]

Negative bitwise complement is a positive number of anti

(2) decimal

\[\left[ X \right]{\rm{ =  }}\left\{ {\begin{array}{*{20}{c}}
{X{\rm{     }}({\rm{0}} \le X{\rm{  <  }}1{\rm{)  }}}\\
{(2 - {2^{ - n + 1}}) + X{\rm{     }}( - 1{\rm{  <  }}X \le 0){\rm{  }}}
\end{array}(\bmod (2 - {2^{ - n + 1}}))} \right.\]

Feature

0 means not unique

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Origin www.cnblogs.com/xumaomao/p/11871267.html