From ceab012b8de1e55676fd5fe6c1b3ca1426882eb6 Mon Sep 17 00:00:00 2001 From: Andre Meyering Date: Wed, 20 Dec 2017 14:53:39 +0100 Subject: [PATCH] [Skript] Fixes --- Bilder/n-bit-Komparator.png | Bin 69285 -> 82722 bytes Kapitel/03_Rechenwerk.tex | 23 ++++++------ Kapitel/04_Speicher.tex | 71 +++++++++++++++++------------------- 3 files changed, 44 insertions(+), 50 deletions(-) diff --git a/Bilder/n-bit-Komparator.png b/Bilder/n-bit-Komparator.png index 85aceff4ae9f699a456ead7e3e7b2cd05c76d0a1..b96b6a09ee33693c24d809b74d25ab7220d1c358 100644 GIT binary patch literal 82722 zcmX_I2RPOJ+ZPd`Y!X6djx8jFQ1(hjHpj?bnUR^jvNu^tcJ_*lI%I~7WRp#WkoW#Q z@Aba_>-k?@k4NYH&Uf7RXWb`UUG)L+W!lSFSXjgg4`ns6ur4%WVPTi!6$|T17xMoLy^bXo@WV@P3Mz7!=7}hX*)H~?G8nP2 z7_k&&r5|}tZ9ez#eDrnvPzN8Jl3>PDV(BaSjQIciuM{r-|6}rCIxGQ|S7Bi&3^S%$(Ozm(FVu8* za3bSD(tPN^O?+t%C9IA^7OcMuk-XM@aZCj^wChbqVQfJp!MSnGQ7Wt$f%PWU1eT=I zxK}Kn*mkid+nUEeRHG8mX+&L&U3?EU5*d?l^Jdn*RHOd>-KbbU7`#_(-WwC2&*9sS z$AmA<B%dS4Q#;pxdn+Wcd>$NRS4eo6 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natürlich nicht alle Vollkonjunktionen benötigt, sonde \newpage % Nur für's Layout \begin{Achtung} - Im folgenden wird fälschlicherweise von einem Aufwand $O(n^2\cdot 2^n)$ ausgegangen. Richtig wäre $O=(n^2\cdot 4^n)$. Herr Röthig hat die $O$-Notation falsch vereinfacht. Der 2015er Jahrgang hat dies \enquote{noch falscher} gemacht und zu $O(4^n)$ vereinfacht. + Im folgenden wird fälschlicherweise von einem Aufwand $O(n^2\cdot 2^n)$ ausgegangen. Richtig wäre $O(n^2\cdot 4^n)$. Herr Röthig hat die $O$-Notation falsch vereinfacht. Der 2015er Jahrgang hat dies \enquote{noch falscher} gemacht und zu $O(4^n)$ vereinfacht. \end{Achtung} Der Hardwareaufwand steigt beim $n$-Bit-\acs{CLA-PA} überexponentiell mit $n$. @@ -473,7 +473,7 @@ $\Rightarrow$ damit ist das $n$ der nicht-\acs{CLA-PA} noch klein $\Rightarrow$ \newpage % Für das Layout \section{Serielladdierer} \index{Serielladdierer} -\textit{Idee}: Angelehnt an die Verfahrensweise des Menschen sollen die Stellen der beiden Summanden nacheinander (und nicht gleichzeitig) addiert werden. Dadurch wird nur \textbf{ein} \acf{VA} und mehrere \acf{SR} benötigt. Daher ist der \acf{SA} ein Schaltwerk, kein Schaltnetz! \autoref{fig:serielladdierer} zeigt das Schaltwerk eines Serielladdierer. +\textit{Idee}: Angelehnt an die Verfahrensweise des Menschen sollen die Stellen der beiden Summanden nacheinander (und nicht gleichzeitig) addiert werden. Dadurch wird nur \textbf{ein} \acf{VA} und mehrere \acf{SR} benötigt. Daher ist der \acf{SA} ein Schaltwerk, kein Schaltnetz! \autoref{fig:serielladdierer} zeigt das Schaltwerk eines Serielladdierers. \begin{figure}[h!] \centering @@ -571,12 +571,12 @@ Der Zeitaufwand für einen $n$-Bit-\acl{SA} beträgt $n$ Taktzyklen, also $O(n)$ \textit{Ist dies wie beim \acs{RC-PA}?} \newline Jein, denn $1$ Taktzyklus dauert deutlich mehr als doppelt solang wie die Berechnung des \acs{VA} (Sicherheitsmargen!). Beispiel: 1 Taktzyklus > \circa{10}~\acs{GLZ} $\Rightarrow$ fünffache Berechnungszeit des \acs{RC-PA} -\subsection{Hardwareaufwand ($N$-Bit-SA)} +\subsection{Hardwareaufwand ($n$-Bit-SA)} \begin{tabular}{@{}l@{}l} 1 \acs{VA} & $ =18$ Transistoren \\ - 2 \acs{D-FF} = $2\cdot 6$ & $ =12$ Transistoren. \hspace*{12.5mm} \textit{(siehe \autoref{fig:schieberegister})} \\ - 3 $n$-Bit-\acs{SR} & $ =3\cdot 6n = 18n$ Transistoren \textit{(siehe \autoref{fig:aufwand_dff})} \\ + 2 \acs{D-FF} = $2\cdot 6$ & $ =12$ Transistoren. \hspace*{12.5mm} \textit{(siehe \autoref{fig:aufwand_dff})} \\ + 3 $n$-Bit-\acs{SR} & $ =3\cdot 6n = 18n$ Transistoren \textit{(siehe \autoref{fig:schieberegister})} \\ Takterzeugung~~ & \textit{(im folgenden nicht näher betrachtet)} \\ \textbf{gesamt} & $18n+30$ Transistoren \end{tabular} @@ -729,7 +729,7 @@ Wie in \autoref{fig:serielladdierer_hw_optimierung} zu sehen ist, wird ein Schie \begin{table} \centering \begin{tabular}{c|c|c} - n & \acs{RC-PA} (18n – 10) & \acs{SA} (12n +36) \\ \midrule + n & \acs{RC-PA} ($18n - 10$) & \acs{SA} ($12n + 36$) \\ \midrule 1 & 8 & 48 \\ 2 & 26 & 60 \\ 3 & 44 & 72 \\ @@ -747,7 +747,7 @@ Break-Even (\enquote{\textit{Gewinnschwelle}}): $18n -10 = 12n + 36 \Rightarrow \textbf{Mögliche Anwendung eines \acl{SA}}: \begin{itemize}[noitemsep] \item nicht im Rechenwerk der \acs{CPU} (aufgrund der Geschwindigkeit)! - \item aber möglicherweise in \enquote{embedded system}, falls \zB Sensordaten sowieso seriell angeliefert werden + \item aber möglicherweise in \enquote{embedded systems}, falls \zB Sensordaten sowieso seriell angeliefert werden \item[$\Rightarrow$] eventuell sind sogar weitere Hardware-Einsparungen möglich! \end{itemize} @@ -865,7 +865,7 @@ Ein $n\times m$-Bit-\acf{PM}, bspw. ein $5\times 4$-Bit-\acl{PM} ist in \autoref \end{figure} \begin{Achtung}[frametitle={Hinweis zur Abbildung}] - Unbedingt auf die \enquote{0} als Eingang achten! Ansonsten gibt es in der Klausur punktabzug! Bei unterschiedlicher Stellenanzahl sind Nullen aufzufüllen. + Unbedingt auf die \enquote{0} als Eingang achten! Ansonsten gibt es in der Klausur punktabzug! Die \enquote{0} ist sogesehen der erste Übertrag. \end{Achtung} \begin{Hinweis} @@ -922,7 +922,7 @@ Demgegenüber sollte bei Verwendung von \acs{RC-PA} besser $n>m$ für geringeren \bigskip \begin{Hinweis}[frametitle={Hinweis für die Klausur}] - Den logarithmischen Aufwand für \acs{CLA-PA} auf \href{https://de.wikipedia.org/wiki/Paralleladdierer_mit_\%C3\%9Cbertragsvorausberechnung}{Wikipedia} nachschauen. Dies wird wahrscheinlich in der Klausur abgefragt! Unserer Variante hat exponentiellen Hardwareaufwand und konstanten Zeitaufwand. Die Variante auf \href{https://de.wikipedia.org/wiki/Paralleladdierer_mit_\%C3\%9Cbertragsvorausberechnung}{Wikipedia} nicht. + Den logarithmischen Aufwand für \acs{CLA-PA} auf \href{https://de.wikipedia.org/wiki/Paralleladdierer_mit_\%C3\%9Cbertragsvorausberechnung}{Wikipedia} nachschauen. Dies wird zwar wahrscheinlich nicht in der Klausur abgefragt, aber er könnte abfragen, welche Alternativen es gibt. Unserer Variante hat exponentiellen Hardwareaufwand und konstanten Zeitaufwand. Die Variante auf \href{https://de.wikipedia.org/wiki/Paralleladdierer_mit_\%C3\%9Cbertragsvorausberechnung}{Wikipedia} nicht. \end{Hinweis} \subsection{Seriellmultiplizierer} \index{Seriellmultiplizierer} @@ -948,7 +948,7 @@ Motivation: Wir wollen eine noch engere Anlehung an das schriftliche Multiplikat \begin{tabular}{c@{}ll} \textbullet~ & $n$-Bit-\acs{PA} $\Rightarrow$ $n$-Bit-\acs{RC-PA} & $\Rightarrow$ $18n-10$ Transistoren \\ - \textbullet~ & $n$ \code{UND} mit jeweils 2 Eingängen & $\Rightarrow$ 2 Transistoren \\ + \textbullet~ & $n$ \code{UND} mit jeweils 2 Eingängen & $\Rightarrow$ $2n$ Transistoren \\ \textbullet~ & $2n$ \acsp{D-FF} & $\Rightarrow$ $12n$ Transistoren \\ \textbullet~ & $2m$-Bit-\acs{SR} & $\Rightarrow$ $12m$ Transistoren \\ \textbullet~ & \multicolumn{2}{@{}l}{Takterzeugung (wird im folgenden nicht berücksichtigt)} @@ -968,8 +968,7 @@ Mindestdauer eines halben Taktzyklus: Berechnungszeit \enquote{innen} & $= 1+1+2n+1=2n+3$ \acs{GLZ} \\ $\Rightarrow$ 1 Taktzyklus & $\gtrsim$ $4n+6$ \acs{GLZ} \\ gesamt: & $\gtrsim m\cdot(4n+6)=4mn+6m=O(nm)$ -\end{tabular}\todo{Kontrollieren} - +\end{tabular} \section{Division} \index{Division} diff --git a/Kapitel/04_Speicher.tex b/Kapitel/04_Speicher.tex index 99dd0a1..647968f 100644 --- a/Kapitel/04_Speicher.tex +++ b/Kapitel/04_Speicher.tex @@ -6,12 +6,12 @@ \begin{table}[ht] \centering - \begin{tabular}{p{29mm}|p{36mm}|p{17mm}|p{34mm}|p{23mm}} - Speicher & von-Neumann-Rechner & Persistenz & Größe & Zugriffszeit \\ \midrule - \acs{CPU}-Register & Zentraleinheit (Rechen- und Steuerwerk) & flüchtig & $<1kB$ Byte & $\approx$ 200ps \\ \midrule - Cache \newline (\enquote{CPU-Cache}) & nicht vorhanden & flüchtig & \circa{4}MB \newline L1$\approx$64KB \newline L2$\approx$512KB & $\approx$ 10ns \\ \midrule - Hauptspeicher/ Primärspeicher & Speicherwerk & flüchtig & \circa{8}GB & $\approx$ 100ns \newline L1 schneller \\ \midrule - Sekundärspeicher & Peripheriegeräte an Ein- und Ausgabewerk & nicht flüchtig & HDD: 3T \newline SSD: 512GB \newline opt.~\acs{LW}: bis~100GB \newline \acs{BLW}: wenige TB & HDD~$\approx10ms$ \newline SSD~$\approx 10\mu s$\newline opt.~\acs{LW}~$\approx 1s$ \newline \acs{BLW}~$\approx 1min$ + \begin{tabular}{p{29mm}|p{36mm}|p{19mm}|p{34mm}|p{23mm}} + \textbf{Speicher} & \textbf{von-Neumann-Rechner} & \textbf{Persistenz} & \textbf{Größe} & \textbf{Zugriffszeit} \\ \midrule + \acs{CPU}-Register & Zentraleinheit (Rechen- und Steuerwerk) & flüchtig & $<1kB$ Byte & $\approx$ 200ps \\ \midrule + Cache \newline (\enquote{CPU-Cache}) & nicht vorhanden & flüchtig & \circa{4}MB \newline L1 $\approx$ 64KB \newline L2 $\approx$ 512KB & $\approx$ 10ns \\ \midrule + Hauptspeicher/ Primärspeicher & Speicherwerk & flüchtig & \circa{8}GB & $\approx$ 100ns \newline L1 schneller \\ \midrule + Sekundärspeicher & Peripheriegeräte an Ein- und Ausgabewerk & nicht flüchtig & HDD: 3T \newline SSD: 512GB \newline opt.~\acs{LW}: bis~100GB \newline \acs{BLW}: wenige TB & HDD~$\approx10ms$ \newline SSD~$\approx 10\mu s$\newline opt.~\acs{LW}~$\approx 1s$ \newline \acs{BLW}~$\approx 1min$ \end{tabular} \caption{Speicherhierarchie und -Daten} \label{tbl:speicherhierarchie} @@ -201,7 +201,7 @@ $\Rightarrow$ sobald das Zugriffsmuster Lokalität aufweist, ergibt sich eine be \hspace*{-5mm} \begin{tabular}{p{32mm}|p{62mm}|p{62mm}} - \textbf{Cachearchitektur} \newline \newline \textbf{Schreibstrategie} + \textbf{Schreibstrategie} \newline \newline \textbf{Cachearchitektur} & \textbf{Write-Bac}k & \textbf{Write-Through} \\ \midrule @@ -226,10 +226,10 @@ $\Rightarrow$ sobald das Zugriffsmuster Lokalität aufweist, ergibt sich eine be \end{figure} \begin{description} - \item[\acf{HSS}] gleich große Speicheranteile des Hauptspeichers. Eine \acs{HSS} sollte $2^m$ \acfp{HSA} beinhalten, um eine einfache Umrechung von \acs{HSS}-Nummern und \acs{HSA} zu ermöglichen. + \item[\acf{HSS}] Gleich große Speicheranteile des Hauptspeichers. Eine \acs{HSS} sollte $2^m$ \acfp{HSA} beinhalten, um eine einfache Umrechnung von \acs{HSS}-Nummern und \acs{HSA} zu ermöglichen. \item[\acf{CL}] Kopie einer \acl{HSS} im Cache \item[Tag] Die um $m$ niederwertigsten Bit gekürzte \acs{HSA}, welche der \acs{HSS}-Nummer entspricht. - \item[Status] Zustandsinfo zur Cache-Line, \zB Valid-Flag und weiter Zustandsinfos abhängig von Verdrängungsstrategie + \item[Status] Zustandsinfo zur Cache-Line, \zB Valid-Flag und weitere Zustandsinfos abhängig von Verdrängungsstrategie \item[Valid-Flag] Die Daten werden im Cache geändert und müssen noch in den \acs{HS} zurückgeschrieben werden (nur bei Write-Back-Schreibstrategie) \end{description} @@ -237,7 +237,7 @@ $\Rightarrow$ sobald das Zugriffsmuster Lokalität aufweist, ergibt sich eine be Jede \acl{HSS} kann in jeder \acl{CL} eingelagert werden (nicht gleichzeitig!) \begin{itemize} - \item[$\Rightarrow$] bei jedem Zugriff auf eine \acf{HSA} muss überprüft werden, ob die gekürzte \acs{HSA} einem der Tags von validen \acl{CL} entspricht! + \item[$\Rightarrow$] bei jedem Zugriff auf eine \acf{HSA} muss überprüft werden, ob die gekürzte \acs{HSA} einem der Tags von validen \aclp{CL} entspricht! \item[$\Rightarrow$] Vergleichen der gekürzten \acs{HSA} mit allen Tags (von validen \acs{CL}) \end{itemize} @@ -263,7 +263,7 @@ Hier: Schaltnetz, welches zwei Zahlen auf Gleichheit, Größer und Kleiner vergl Möchte man eine Wertetabelle für einen $n$-Bit-Komparator erstellen, sieht man, dass zu viele Zeilen in der Wertetabelle ($2^{2n}$\ldots) sind $\Rightarrow$ besser mit kaskadierbaren 1-Bit-Komparatoren \textsf{\textbf{Komparator für Gleichheit}} \newline -\textit{Hinweis}: im Cache reicht der Vergleich auf Gleichheit. \autoref{fig:cache_komparator_3} zeigt 1-Bit-Komparatoren für einen Gleichheits-Komparator. +\textit{Hinweis}: Im Cache reicht der Vergleich auf Gleichheit. \autoref{fig:cache_komparator_3} zeigt 1-Bit-Komparatoren für einen Gleichheits-Komparator. \begin{figure}[!ht] \centering \includegraphics[width=9cm]{./Bilder/Aufwand_Komparator.png} @@ -359,8 +359,8 @@ Viele Paare von \acs{HSS} können nicht gleichzeitig im Cache gehalten werden (b \textbf{Abhilfe}: \acf{nWAC} \subsection{$n$-Wege-Assoziativ-Cache} \index{Cache!$n$-Wege-Assoziativ-Cache} -Für jede \acs{HSS} gibt es genau $n$ \acl{CL}, in welche die \acs{HSS} eingelagert werden kann. -Realisierung über $n$ \acs{DMC}, welche alle jeweils gleich aufgebaut sind. +Für jede \acs{HSS} gibt es genau $n$ \aclp{CL}, in welche die \acs{HSS} eingelagert werden kann. +Die Realisierung findet über $n$ \acs{DMC} statt, welche alle jeweils gleich aufgebaut sind. \subsection{Kollision} @@ -411,7 +411,7 @@ Wenn eine \acs{HSS} in den Cache eingelagert werden soll, muss eine andere aus d \bigskip \begin{Hinweis} - Die Größe eines Speicherwertes in Bit wird nicht definiert und ist auch unerheblich für die folgenden Überlegungen + Die Größe eines Speicherwertes bzw. Wortes in Bit wird nicht definiert und ist auch unerheblich für die folgenden Überlegungen \end{Hinweis} \begin{figure}[!ht] @@ -504,19 +504,16 @@ Wenn eine \acs{HSS} in den Cache eingelagert werden soll, muss eine andere aus d $\Rightarrow$ Hit in Cache A \acs{CL}-Nr. 2 \end{paracol} -\columnratio{0.5} -\begin{paracol}{2} - \textbf{angefragte \acs{HSA}}: $0675_{10}$ - \begin{center} - $\underbrace{~0~0~1~0~1~}_\text{Tag}\underbrace{~0~~~1~~~0~}_\text{\acs{CL}-Nr. 2}\underbrace{~0~0~1~1~}_\text{Pos. in \acs{CL} (3)}$ - \end{center} - Tag in \acs{CL}-Nr. 2 von Cache A und Cache B sind verschieden vom angefragten Tag. - - $\Rightarrow$ Miss $\Rightarrow$ sogar Kollision - - $\Rightarrow$ Verdrängung notwendig - \switchcolumn -\end{paracol} +\textbf{angefragte \acs{HSA}}: $0675_{10}$ + + $\underbrace{~0~0~1~0~1~}_\text{Tag}\underbrace{~0~~~1~~~0~}_\text{\acs{CL}-Nr. 2}\underbrace{~0~0~1~1~}_\text{Pos. in \acs{CL} (3)}$ + +Tag in \acs{CL}-Nr. 2 von Cache A und Cache B \newline +sind verschieden vom angefragten Tag. + +$\Rightarrow$ Miss $\Rightarrow$ sogar Kollision \newline +$\Rightarrow$ Verdrängung notwendig + \subsection{Verdrängungsstrategie} \label{sec:verdraengungsstrategie} \index{Cache!Verdrängungsstrategie} @@ -563,7 +560,7 @@ Ständig genutzte Datenstücke werden genauso schnell verdrängt wie Daten, die Bei der \acf{LRU} Strategie wird die \acl{HSS}, auf welche am längsten nicht zugegriffen wurde, verdrängt. \textit{Aufwand}: \newline -Timestamp mit Update bei jedem Zugriff $\Rightarrow$ Die Suche bei Verdrängung ist zu aufwändig +Timestamp mit Update bei jedem Zugriff $\Rightarrow$ Die Suche bei Verdrängung ist zu aufwändig! \textit{Besser}:\newline Verwaltung als \textit{doppelt} verkettete Liste, \dash Zeiger auf Vorgänger \textit{und} Nachfolger in jeder \acs{CL}. Globalen Zeiger auf ersten und letzten Eintrag. @@ -588,8 +585,6 @@ Bei der \acf{LFU} Strategie wird die \acl{HSS} verdrängt, welche bisher am selt $\Rightarrow$ Bei Verdrängung aufwändige Berechnung und Suche \end{paracol} -\newpage % Nur für's Layout - \textit{Problem (Zugriffsmuster)}: \newline Neu eingelagerte Seiten werden schnell wieder verdrängt, wenn sich der Zugriffszähler am Anfang nicht schnell genug erhöht und andere etablierte Seiten eine höhere Häufigkeit aufgrund vieler \enquote{alter} Zugriffe aufweisen. @@ -601,8 +596,8 @@ Mehrere Zugriffszähler in jeder \acs{CL} für die letzten $i$ Zeitscheiben. Dividieren ist damit überflüssig (alle Zeitscheiben sind gleich lang): Addition der mit $2^j$ gewichteten Zähler als \enquote{Häufigkeit} ($j=i-1$ für jüngste Zeitscheiben, $j=0$ für älteste Zeitscheibe). \textit{Weiterhin}: \newline -Bei der Verdrängung gibt ein Problem bei der Suche nach der niedrigsten \enquote{Häufigkeit}. \newline -$\Rightarrow$ evtl. Lösung über eine bei Beginn jedes Zeitslots neu aufzubauende verkettete Liste. \newline +Bei der Verdrängung gibt es ein Problem bei der Suche nach der niedrigsten \enquote{Häufigkeit}. \newline +$\Rightarrow$ evtl. Lösung über eine bei Beginn jeden Zeitslots neu aufzubauende verkettete Liste. \newline \phantom{$\Rightarrow$ }Hier gibt es viel Platz für Optimierungen der \acs{CPU}-Hersteller. \subsection{Cache bei Mehrprozessor-/Mehrkernsystemen} \index{Mehrkernprozessor} @@ -620,7 +615,7 @@ In \autoref{fig:cpu_mehrprozessor} besitzt jeder Kern einen eigenen Cache. Mögl \begin{tabular}{@{}cp{7.6cm}|cp{7.6cm}} & \textbf{gemeinsamer Cache} & & \textbf{getrennter Cache} \\ \midrule - $\oplus$ & dieselben Daten für beide Kerne benötigt bedeutet nur einmaliges Einlagern im Cache (Platzvorteil). + $\oplus$ & dieselben Daten für beide Kerne benötigt/bedeutet nur einmaliges Einlagern im Cache (Platzvorteil). & $\ominus$ & Dieselben Daten müssen ggf. mehrfach in den Caches gehalten werden. \\ [4ex] @@ -658,14 +653,14 @@ Mehrere 1-Bit-Worte hängen an der selben Datenleitung, werden aber über unters \begin{figure}[!ht] \centering - \includegraphics[width=\textwidth-4cm]{./Bilder/HS_Kondensator.png} + \includegraphics[width=\textwidth-52mm]{./Bilder/HS_Kondensator.png} \caption{Hauptspeicher -- 1-Bit-Kondensatorspeicher} \label{fig:hs_kondensator} \end{figure} Um aus der $n$-Bit-\acs{HSA} $2^n$ Select-Leitungen zu erzeugen, welche die Bits abfragen, ist ein $n:2^n$-Decoder notwendig. -In \autoref{fig:4_16_dekoder} wird ein 4:16-Decoder mit entsprechender Wertetabelle gezeigt. +In \autoref{fig:4_16_dekoder} wird ein $4:16$-Decoder mit entsprechender Wertetabelle gezeigt. \begin{figure}[!ht] \centering @@ -756,7 +751,7 @@ Eine matrixförmige Speicherorganisation: zweidimensionale Anordnung der Speiche $a_3a_2$ gibt die Zeilennummer an und $a_1a_0$ die Spaltennummer. Somit reicht es statt eines 4:16-Decoders einen 2:4~Zeilen- und einen 2:4~Spalten-Decoder zu verwenden. \textbf{Aufwand} \newline -Anstatt wie bei einem 4:16-Decoder mit 64 Transistoren beträgt der Aufwand bei zwei 2:4-Decodern mit $2\cdot 8$ Transistoren = 16 Transistoren. +Anstatt wie bei einem $4:16$-Decoder mit 64 Transistoren beträgt der Aufwand bei zwei $2:4$-Decodern mit $2\cdot 8$ Transistoren = 16 Transistoren. 64-Bit \acs{HSA}: als $64:2^{64}$ Decoder: $2^{70}$ Transistoren @@ -792,7 +787,7 @@ Statt eines Spalten-Decoders werden die Datenleitungen aller Speicherbits einer \label{fig:schaltnetz_MUX} \end{figure} -Realisierung über $2:4$ Decoder sowie 4 \code{UND} mit jeweils 2 Eingängen und ein \code{ODER} mit 4 Eingängen +Realisierung über $2:4$ Decoder sowie 4 \code{UND} mit jeweils 2 Eingängen und ein \code{ODER} mit 4 Eingängen. $2^n:1$ MUX: \newline \hspace*{5mm}ein $n:2^n$ Decoder \newline @@ -806,7 +801,7 @@ Vor den Multiplexer kann ein Cache geschaltet werden, sodass eine ganze \acs{HSS \subsection{Gründe für Matrixorganisation} \begin{enumerate}[noitemsep] - \item weniger Aufwand für Adresscodecodierung + \item weniger Aufwand für Adressdecodierung \item Einlesen einer ganzen \acs{HSS} (=Matrixzeile) in den Cache \item zeilenweiser Refresh des \acs{HS} (wortweiser Refresh-Zyklus dauert viel zu lange) \end{enumerate} \ No newline at end of file