Floating Point(浮点数)

Fractional Binary Numbers

$$ d = \sum_{i=-n}^{m}10^i \times d_i $$

$$ b=\sum_{i=-n}^{m}2^i{\times}b_i $$

Floating-Point Type

$$ V=(-1)^{8}{\times}M{\times}2^{E} $$

Normalized Values

规格化的值

s $e_7$ $e_6$ $e_5$ $e_4$ $e_3$ $e_2$ $e_1$ $e_0$ $f_{31}$ $…$ $f_0$

$$ \underbrace{e_{7}=1|e_{6}=1|e_{5}=1|e_{4}=1|e_{3}=1|e_{2}=1|e_{1}=1|e_{0}=0}{e{max}=254} $$

$$ \underbrace{e_7=0|e_6=0|e_5=0|e_4=0|e_3=0|e_2=0|e_1=0|e_0=1}{e{min}=1} \\ $$

$$ E=e-bias \\ bias(float)=2^{8-1}-1=127 \\ E_{min}=-126 \ E_{max}=127 $$

Denormalized Values

非规格化的值

Special Values

特殊值

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