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