diff --git a/复习资料/A.aux b/复习资料/A.aux index d1057a5..94189bf 100644 --- a/复习资料/A.aux +++ b/复习资料/A.aux @@ -10,8 +10,9 @@ \@writefile{toc}{\contentsline {subsection}{\numberline {1.4}GDB查看数据}{1}{subsection.1.4}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.5}浮点数}{2}{subsection.1.5}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.1}规格化数 $ \text {exp} \ne 0$ 且 $\text {exp} \ne 11 \dots 1$}{2}{subsubsection.1.5.1}\protected@file@percent } -\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.2}非规格化数 $\text {exp} = 0 $}{2}{subsubsection.1.5.2}\protected@file@percent } -\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.3}舍入(到偶数)}{2}{subsubsection.1.5.3}\protected@file@percent } +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.2}非规格化数 $\text {exp} = 0$}{2}{subsubsection.1.5.2}\protected@file@percent } +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.3}特殊值 $\text {exp} = 11 \dots 1$}{2}{subsubsection.1.5.3}\protected@file@percent } +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.4}舍入(到偶数)}{2}{subsubsection.1.5.4}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {2}程序的机器级表示}{3}{section.2}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}计算数组元素的地址}{3}{subsection.2.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}其他内容}{3}{subsection.2.2}\protected@file@percent } diff --git a/复习资料/A.pdf b/复习资料/A.pdf index ff7e01f..eef84d7 100644 Binary files a/复习资料/A.pdf and b/复习资料/A.pdf differ diff --git a/复习资料/A.tex b/复习资料/A.tex index 71a024b..9b8393e 100644 --- a/复习资料/A.tex +++ b/复习资料/A.tex @@ -37,7 +37,8 @@ \lstset{basicstyle=\ttfamily,columns=fullflexible} -\columnseprule=0.4pt +\setlength{\columnsep}{1cm} +\setlength{\columnseprule}{0.4pt} \begin{document} @@ -70,45 +71,45 @@ T: 用 $n$ 位表示数字 \begin{multicols}{2} \qquad 对应正数补码的“各位取反、末位加1” \begin{align*} - +23 & = 00010111 \\ - \text{按位取反} & = 11101000 \\ - & + \hspace{1.8cm} 1 \\ - -23_{\text{补码}} & = 11101001 + +23 & = \texttt{00010111} \\ + \text{按位取反} & = \texttt{11101000} \\ + & + \hspace{0.3em}\phantom{0000000}\texttt{1} \\ + -23_{\text{补码}} & = \texttt{11101001} \end{align*} \columnbreak \qquad 模($2^n$)减去该负数的绝对值 \begin{align*} - 100000000 & \\ - -00010111 & \\ - \rule{2.5cm}{0.02em} \\ - 11101001 + & \texttt{100000000} \\ + - \hspace{0.5em} & \phantom{\texttt{0}}\texttt{00010111} \\[-1em] + & \hspace{-1em}\rule{2.5cm}{0.02em} \\[-0.5em] + & \phantom{\texttt{0}}\texttt{11101001} \end{align*} \end{multicols} \subsection{GDB查看数据} + +\texttt{>(gdb) x/4xb} \\[1em] +\begin{minipage}{12cm} \begin{multicols}{2} -\texttt{>(gdb) x/4xb} \\ -b - byte (8-bit value)\\ -h - halfword (16-bit value) \\ -w - word (32-bit value) \\ -g - giant word (64-bit value) - -\columnbreak - -o - octal \\ -x - hexadecimal \\ -d - decimal \\ -u - unsigned decimal \\ -t - binary \\ -f - floating point \\ -a - address \\ -c - char \\ -s - string \\ -i - instruction + \texttt{b} - byte (8-bit value) \\ + \texttt{h} - halfword (16-bit value) \\ + \texttt{w} - word (32-bit value) \\ + \texttt{g} - giant word (64-bit value) \\ + \texttt{o} - octal \\ + \texttt{x} - hexadecimal \\ + \texttt{d} - decimal \\ + \texttt{u} - unsigned decimal \\ + \texttt{t} - binary \\ + \texttt{f} - floating point \\ + \texttt{a} - address \\ + \texttt{c} - char \\ + \texttt{s} - string \\ + \texttt{i} - instruction \end{multicols} +\end{minipage} \newpage @@ -127,12 +128,14 @@ i - instruction 浮点数表示为 $(-1)^s \cdot M \cdot 2^E$ -\InsertBoxR{1}{\tcboxmath{\begin{matrix} +\InsertBoxR{0}{\tcboxmath{\begin{matrix} \multicolumn{2}{c}{\text{偏置值 Bias}} \\ \texttt{float} & 127 \\ \texttt{double} & 1023 \\ \end{matrix}}\hspace{3cm}} - + +\vspace{-1em} + \subsubsection{规格化数 $ \text{exp} \ne 0$ 且 $\text{exp} \ne 11 \dots 1$} $\text{(unsigned)} \ \text{exp} \ = \ E \ + \text{Bias}$ @@ -161,37 +164,69 @@ $\text{Bias (偏置值)} = 2^{k-1}-1$ , k 为 $exp$ 的二进制位数 \end{matrix}\) \columnbreak - 例2:二进制浮点数$\rightarrow$十进制数\\ - 无符号数，4位阶码(Bias=7)，3个小数位 - \begin{align*} - 1001 \quad 111 \\ - exp \quad frac \\ - \text{计算E:} \\ - E &= exp - Bias \\ + 例2: 二进制浮点数$\rightarrow$十进制数 + + 无符号数，4位阶码(Bias\(=7\))，3个小数位 \\ + + \quad \(\begin{matrix} + 1001 & 111 \\ + \text{exp} & \text{frac} + \end{matrix}\) \\[0.5em] + + \(\begin{aligned} + \text{计算} \space E &= \text{exp} - \text{Bias} & \\ &= 1001_2 - 7_{10} \\ - &= 2_{10} \\ - \text{计算M:} \\ - M = 1.\underbar{frac} &= 1.\underbar{111} \\ - \text{化为十进制:} \\ - 1.111 \times 2^2 &= 111.1_2 \quad \text{小数点右移2位} \\ - &= 7\frac{1}{2} = \frac{15}{2} - \end{align*} + &= 2_{10} + \end{aligned}\) \\[0.5em] + + 计算 \(M = 1.\underbar{frac} = 1.\underbar{111}\) \\[0.5em] + + 化为十进制: + + \(\begin{aligned} + 1.111 \times 2^2 & = 111.1_2 \quad \text{小数点右移2位} \\ + & = \frac{15}{2} = 7.5 + \end{aligned}\) \end{multicols} -\InsertBoxR{1}{\tcboxmath{\begin{matrix} +\InsertBoxR{0}{\tcboxmath{\begin{matrix} \text{非规格化数} \ E = 1 - \text{Bias} \\ \begin{matrix} \texttt{float} & -126 \\ \texttt{double} & -1022 \\ \end{matrix} -\end{matrix}}\hspace{2cm}} +\end{matrix}} +\hspace{2cm}} +\vspace{-5mm} -\subsubsection{非规格化数 $\text{exp} = 0 $} +\vspace{-0.3em} + +\subsubsection{非规格化数 $\text{exp} = 0$} frac \(= 00\dots0\) 表示 0 frac \(\ne 00\dots0\) 表示接近 0 的小数 $(-1)^s \cdot M \cdot 2^{E}$ +\vspace{-0.3em} + +\subsubsection{特殊值 $\text{exp} = 11 \dots 1$} + +\begin{multicols}{2} + +frac \(= 00\dots0\) 表示 \(\infty\) + +frac \(\ne 00\dots0\) 表示 NaN + +\columnbreak + +\(1.0 / 0.0 = −1.0 / −0.0 = + \infty\) + +\(1.0 / −0.0 = - \infty\) + +\(\sqrt{–1.0} = \infty - \infty = \infty \times 0 = \text{NaN}\) + +\end{multicols} + \subsubsection{舍入(到偶数)} \begin{table}[h] @@ -276,7 +311,4 @@ D 当前所有定义符号的集合\\ PC相对地址下重定位值计算公式：\\ \texttt{ADDR(r.symble)-((ADDR(.text)+r.offset)-r.addend)}\\ 在asm中表示为 \texttt{4004de: e8 \underbar{05 00 00 00} \quad callq 4004e8 } - -\pagebreak - \end{document}