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RS: RS-Bearbeitungen hinzugefügt
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Jim Martens
202
rs/RS_G1_B11_Martens_Kornblum.tex
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202
rs/RS_G1_B11_Martens_Kornblum.tex
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\documentclass[10pt,a4paper,oneside,ngerman,numbers=noenddot]{scrartcl}
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\usepackage[T1]{fontenc}
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\usepackage[utf8]{inputenc}
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\usepackage[ngerman]{babel}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{paralist}
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\usepackage{qtree}
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\usepackage[locale=DE,exponent-product=\cdot ,detect-all]{siunitx}
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\usepackage{tikz}
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\usepackage[scaled=0.78]{luximono}
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\usepackage{listings}
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\usepackage{subfigure}
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\usetikzlibrary{automata,matrix,fadings,calc,positioning,decorations.pathreplacing,decorations.text,arrows}
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\pagenumbering{arabic}
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\def\thesection{11.\arabic{section})}
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\def\thesubsection{(\alph{subsection})}
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\def\thesubsubsection{(\arabic{subsubsection})}
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\renewcommand{\labelenumi}{(\roman{enumi})}
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\hyphenation{Nach-komma-stel-len}
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\lstnewenvironment{java}[1][]{%
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\lstset{basicstyle=\ttfamily ,backgroundcolor=\color[gray]{.95},columns=flexible,fontadjust=true,language=Java,tabsize=4,numbers=none,#1}%
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}{%
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}
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\graphicspath{{D:/Users/Jim-Studium/Pictures/Studium/RS/}}
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\tikzstyle{huffmanNodes}=[matrix of nodes,
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nodes={circle,thin,draw=black!20,minimum size=10mm,text height=1.5ex,text depth=.25ex,inner sep=-10pt}]
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\tikzstyle{huffmanBase}=[matrix of nodes,
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nodes={minimum size=10mm,text height=1.5ex,text depth=.25ex,inner sep=-10pt}]
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\begin{document}
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\author{Jim Martens (Matrikelnummer 6420323) \and Marlo Kornblum (Matrikelnummer 6427301)}
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\title{Rechnerstrukturen Aufgabenblatt 11}
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\maketitle
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\section{} %11.1
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\subsection{} %a
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30
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\subsection{} %b
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40
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\subsection{} %c
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50
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\subsection{} %d
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30
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\subsection{} %e
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40
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\section{} %11.2
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\begin{figure}[h]
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7 Befehle mit einer 5-bit Registernummer und einer 24-bit Adresse:\\
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\begin{tikzpicture}
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\draw (0,0) -- +(12,0); %untere Kante
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\draw (0,0) -- +(0,0.5); %linke Kante
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\draw (0,0.5) -- +(12,0); %obere Kante
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\draw (12,0) -- +(0,0.5); %rechte Kante
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\draw (1.5,0) -- +(0,0.5); %rechte Kante von Opcode
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\draw (4.0,0) -- +(0,0.5); %rechte Kante der Reg-nr.
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\node at ++(0.7, 0.2) (opcode) {Opcode}; %Opcode
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\node at ++(2.2, 0.2) (regNr) {Reg-Nr.}; %Reg-Nr.
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\node at ++(6.2, 0.2) (address) {Adresse}; %Adresse
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\node at ++(0.2,-0.4) (31) {$31$};
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\node at ++(1.3,-0.4) (29) {$29$};
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\node at ++(1.7,-0.4) (28) {$28$};
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\node at ++(4.8,-0.4) (24) {$24$};
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\node at ++(5.2,-0.4) (23) {$23$};
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\node at ++(11.8,-0.4) (0) {$0$};
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\end{tikzpicture}
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\end{figure}
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\begin{figure}[h]
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100 Befehle mit zwei 5-bit Registernummern und einem Adressoffset:\\
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\begin{tikzpicture}
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\draw (0,0) -- +(12,0); %untere Kante
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\draw (0,0) -- +(0,0.5); %linke Kante
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\draw (0,0.5) -- +(12,0); %obere Kante
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\draw (12,0) -- +(0,0.5); %rechte Kante
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\draw (1.5,0) -- +(0,0.5); %rechte Kante von Opcode1
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\draw (5.0,0) -- +(0,0.5); %rechte Kante von Opcode2
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\draw (7.5,0) -- +(0,0.5); %rechte Kante von Reg-Nr.
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\draw (10.0,0) -- +(0,0.5); %rechte Kante von Reg-Nr. 2
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\node at ++(0.7,0.2) (opcode1) {$111$}; %Opcode1
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\node at ++(2.2,0.2) (opcode2) {Opcode}; %Opcode2
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\node at ++(5.7,0.2) (regNr) {Reg-Nr.}; %Reg-Nr.
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\node at ++(8.4,0.2) (regNr2) {Reg-Nr. 2}; %Reg-Nr. 2
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\node at ++(10.7,0.2) (offset) {Offset}; %Adressoffset
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\node at ++(0.2,-0.4) (31) {$31$};
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\node at ++(1.3,-0.4) (29) {$29$};
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\node at ++(1.7,-0.4) (28) {$28$};
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\node at ++(4.8,-0.4) (22) {$22$};
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\node at ++(5.2,-0.4) (21) {$21$};
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\node at ++(7.3,-0.4) (17) {$17$};
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\node at ++(7.7,-0.4) (16) {$16$};
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\node at ++(9.8,-0.4) (12) {$12$};
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\node at ++(10.2,-0.4) (11) {$11$};
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\node at ++(11.8,-0.4) (0) {$0$};
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\end{tikzpicture}\\
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Es stehen maximal $12$ Bit für den Adressoffset zur Verfügung.
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\end{figure}
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\begin{figure}[h]
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30 Befehle ohne Adressen oder Registerangaben:\\
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\begin{tikzpicture}
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\draw (0,0) -- +(12,0); %untere Kante
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\draw (0,0) -- +(0,0.5); %linke Kante
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\draw (0,0.5) -- +(12,0); %obere Kante
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\draw (12,0) -- +(0,0.5); %rechte Kante
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\draw (1.5,0) -- +(0,0.5); %rechte Kante von Opcode1
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\draw (5.0,0) -- +(0,0.5); %rechte Kante von Opcode2
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\draw (7.5,0) -- +(0,0.5); %rechte Kante von Opcode3
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\node at ++(0.7,0.2) (opcode1) {$111$}; %Opcode1
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\node at ++(2.2,0.2) (opcode2) {$1111111$}; %Opcode2
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\node at ++(5.7,0.2) (opcode3) {Opcode}; %Opcode3
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\node at ++(8.5,0.2) (undefined) {unbenutzt}; %unbenutzt
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\node at ++(0.2,-0.4) (31) {$31$};
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\node at ++(1.3,-0.4) (29) {$29$};
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\node at ++(1.7,-0.4) (28) {$28$};
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\node at ++(4.8,-0.4) (22) {$22$};
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\node at ++(5.2,-0.4) (21) {$21$};
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\node at ++(7.3,-0.4) (17) {$17$};
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\node at ++(7.7,-0.4) (16) {$16$};
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\node at ++(11.8,-0.4) (0) {$0$};
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\end{tikzpicture}
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\end{figure}
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Für die ersten sieben Befehle wird ein dreistelliger Opcode benötigt, um sie voneinander unterscheiden zu können. Da 8 Codes maximal möglich sind, aber nur 7 benutzt werden, kann die achte Kombination (111) als Differenzierung zur zweiten Befehlsanzahl fungieren.
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Bei dieser wird ein siebenstelliger Opcode benötigt, um die 100 Befehle voneinander unterscheiden zu können. Ein sechsstelliger Opcode würde nur $64$ Befehle unterstützen.
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Die 5-bit Registernummern sind in den beiden ersten Fällen vorhanden und verbrauchen beide Male 5-bit.
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Der Adressoffset benutzt schließlich die übrigen unbenutzten Stellen.
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Die 30 restlichen Befehle werden von den vorigen beiden Befehlstypen durch die drei Einsen der ersten Befehle und weiteren 7 Einsen der zweiten Befehle (beide Male sind diese Werte ohne Benutzung) unterschieden. Innerhalb dieser 30 Befehle wird mithilfe eines 5-bit Opcodes zwischen den einzelnen Befehlen unterschieden.
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\section{} %11.3
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Wir nehmen an, dass anstatt 12-bit tatsächlich die 8-bit Kodierung gemeint war. Schließlich kann der Immediate-Wert nur 8-bit darstellen. Daher werden wir im Folgenden die Werte in 8-bit Kodierung darstellen.
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\subsection{} %a
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$185_{10} = 10111001_{2}, rot = 16$
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\subsection{} %b
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$355_{10} = 101100011_{2}$
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Kann nicht dargestellt werden, da der Immediate-Wert nur 8-bit nutzen kann. Hier werden jedoch 9-bit benutzt.
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\subsection{} %c
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$1576_{10} = 11000101_{2}, rot = n.e.$
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Kann nicht dargestellt werden, da durch Rotierung des Immediate-Wertes nicht die nötige Position erreicht werden kann. Es würde eine ungerade Anzahl an Schiebeoperationen erfordern, was hier nicht möglich ist.
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\subsection{} %d
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$1584_{10} = 01100011_{2}, rot = 14$
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\subsection{} %e
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$2415919104_{10} = 00001001_{2}, rot = 2$
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\section{} %11.4
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\subsection{} %a
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0-Adress-Maschine:\\
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PUSH F\\
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PUSH E\\
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PUSH D\\
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MUL\\
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ADD\\
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PUSH C\\
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PUSH B\\
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MUL\\
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PUSH A\\
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SUB\\
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DIV\\
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POP R\\
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\\
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1-Adress-Maschine:\\
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LOAD D\\
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MUL E\\
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ADD F\\
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STORE G\\
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LOAD B\\
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MUL C\\
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STORE H\\
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LOAD A\\
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SUB H\\
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DIV G\\
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STORE R\\
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\\
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2-Adress-Maschine:\\
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MOV G,D\\
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MUL G,E\\
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ADD G,F\\
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MOV H,B\\
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MUL H,C\\
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SUB A,H\\
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DIV A,G\\
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MOV R,A\\
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\\
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3-Adress-Maschine:\\
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LOAD X,D\\
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LOAD Y,E\\
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MUL X,X,Y\\
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LOAD Y,F\\
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ADD X,X,Y\\
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LOAD Y,B\\
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LOAD Z,C\\
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MUL Y,Y,Z\\
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LOAD Z,A\\
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SUB Z,Z,Y\\
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DIV Z,Z,X\\
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STORE R,Z\\
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\subsection{} %b
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Die 0-Adress-Maschine verbraucht $212$ Bit. Die 1-Adress-Maschine verbraucht $236$ Bit. Die 2-Adress-Maschine verbraucht $208$ Bit. Die 3-Adress-Maschine verbraucht $220$ Bit.
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Die 2-Adress-Maschine verbraucht am wenigsten Bit.
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\end{document}
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