CS61C | lecture5
浮点数的表示
用一个小数点作为边界分隔整数部分和小数部分。
10.101
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2.62
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10
10.1010_{2}=1\times2^1+1\times2^{-1}+1\times2^{-3}=2.625_{10}
10.10102=1×21+1×2−1+1×2−3=2.62510
Scientific Notation(Binary)
单精度
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+{1.xxx...x_{2}\times2^{yyy...y}}_2
+1.xxx...x2×2yyy...y2
Bias = 127
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127
(-1)^S \times (1.\textcolor{red}{Significand})\times 2^{\textcolor{blue}{Exponent}-127}
(−1)S×(1.Significand)×2Exponent−127
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\begin{aligned} &\textcolor{green}{0}\textcolor{blue}{011~~1111~~1}\textcolor{red}{100~~0000~~0000~~0000~~0000~~0000}_2 \\ =&(-1)^{\textcolor{green}{0}}\times(1.\textcolor{red}{1}_2) \times 2^{\textcolor{blue}{127} - 127} \\ =&(1.\textcolor{red}{1}_2) \times 2(\textcolor{blue}{0}) \\ \\ &1.1_2 = 1\times 2^0 + 1 \times 2^{-1} = 1.5_{10} \\ \end{aligned}
==0011 1111 1100 0000 0000 0000 0000 00002(−1)0×(1.12)×2127−127(1.12)×2(0)1.12=1×20+1×2−1=1.510
注意有一个隐式的 1 在 Significand 前面，所以是
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1.5_{10}
1.510 而不是
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0.5_{10}
0.510
双精度
