From 0bd2473b5ca869e4a47524390f02d155781398a9 Mon Sep 17 00:00:00 2001 From: alexander Date: Tue, 10 Feb 2026 23:06:36 +0100 Subject: [PATCH] Extend CT --- src/cheatsheets/CT.typ | 228 +++++++++++++++++++++++++++- src/images/ct/betragUndVorzeich.png | Bin 0 -> 96426 bytes src/images/ct/einerKomplement.png | Bin 0 -> 95922 bytes src/images/ct/zweierKomplement.png | Bin 0 -> 95984 bytes src/lib/bit_fields.typ | 40 +++++ 5 files changed, 265 insertions(+), 3 deletions(-) create mode 100644 src/images/ct/betragUndVorzeich.png create mode 100644 src/images/ct/einerKomplement.png create mode 100644 src/images/ct/zweierKomplement.png create mode 100644 src/lib/bit_fields.typ diff --git a/src/cheatsheets/CT.typ b/src/cheatsheets/CT.typ index ef4e18c..253af4b 100644 --- a/src/cheatsheets/CT.typ +++ b/src/cheatsheets/CT.typ @@ -1,5 +1,6 @@ #import "../lib/styles.typ" : * #import "../lib/common_rewrite.typ" : * +#import "../lib/bit_fields.typ" : * #import "@preview/cetz:0.4.2" #set page( @@ -24,8 +25,8 @@ #let Allgemein = color.hsl(105.13deg, 92.13%, 75.1%) #let colorProgramming = color.hsl(330.19deg, 100%, 68.43%) #let colorNumberSystems = color.hsl(202.05deg, 92.13%, 75.1%) -// #let colorVR = color.hsl(280deg, 92.13%, 75.1%) -// #let colorAbbildungen = color.hsl(356.92deg, 92.13%, 75.1%) +#let colorMMIX = color.hsl(280deg, 92.13%, 75.1%) +#let colorRandomShit = color.hsl(356.92deg, 92.13%, 75.1%) // #let colorGruppen = color.hsl(34.87deg, 92.13%, 75.1%) @@ -48,7 +49,98 @@ ] #bgBlock(fill: colorNumberSystems)[ - #subHeading(fill: colorNumberSystems)[Einer-Kompilment, Zweier-Kompliment, Float (IEEE 754)] + #subHeading(fill: colorNumberSystems)[Fixed Point] + + #table( + columns: 17, + fill: (x, y) => if calc.rem(x, 2) == 1 { tableFillLow } else { tableFillHigh }, + + .. for i in range(0,17) { + ([$2^#i$],) + }, + .. for i in range(0,17) { + ($#calc.pow(2,i)$,) + } + ) + + #columns(2, [ + *Vorzeichen und Betrag:* + + #grid( + columns: (2fr, 1fr), + [ + $x = (-1)^"sign-bit" dot "Betrag"$ + + $0 -> "positiv", 1 -> "negativ"$ + + Range: \ $(-2^(n-1) - 1) dot 2^r$ bis $(2^(n-1) - 1) dot 2^r$ + + Achtung: $plus.minus 0$ + ], + image("../images/ct/betragUndVorzeich.png", width: 2cm) + ) + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + *Einer-Komplement* + + #grid( + columns: (2fr, 1fr), + [ + $x = (-1)^"sign-bit" dot "Betrag"$ + + $0 -> "positiv normaler Betrag"$ + + $1 -> "negativ INVERT. Betrag"$ + + Range: \ + $(-2^(n-1) - 1) dot 2^r$ bis $(2^(n-1) - 1) dot 2^r$ + + Achtung: $plus.minus 0$ + ], + image("../images/ct/einerKomplement.png", width: 2cm) + ) + #colbreak() + + *Zweier-Komplement* + + #grid( + columns: (2fr, 1fr), + [ + $x = (-1)^"sign-bit" dot "Betrag"$ + + $0 -> "positiv"$ + + $1 -> "negativ"$ + + Range: \ $(-2^(n-1)) dot 2^r$ bis $(2^(n-1) - 1) dot 2^r$ + + Positiv: Normal Binär Kodierung + + Negativ: #raw("Invertiert(Binär) + 1") + + ], + image("../images/ct/zweierKomplement.png", width: 2cm) + ) + + #line(length: 100%, stroke: (thickness: 0.2mm)) + + *Radix / Fixed Point* + + $r = 0$ Normal Falle, nix änder sich + + $r > 0$ : Komma nach Rechts und Nullen auffüllen \ + Bsp. $r = 3 quad ->$ #raw("xxxxxxx000.") + + $r < 0$ : Komma nach Links verschieben \ + Bsp: $r = -4 quad ->$ #raw("xxxxx.xxxx") + + ]) + ] + + #colbreak() + #bgBlock(fill: colorNumberSystems)[ + #subHeading(fill: colorNumberSystems)[Float (IEEE 754)] *Float (IEEE 754)* @@ -133,11 +225,46 @@ content((cell_size*(total_bits), -0.2), anchor: "south", raw(str(0)), angle: 90deg) }) + + $x = (-1)^"sign" dot #raw("1.[mantisse]") dot 2^(("exponent" - k))$ + + #grid( + columns: (auto, auto), + column-gutter: 5mm, + row-gutter: 2mm, + $"float32"&, k = 127 &= #raw(" 111 1111") "(7 x Einser)" \ + "float64"&, k = 1023 &= #raw("11 1111 1111") "(10 x Einser)"$ + ) + + *Spezial Cases* + #table( + columns: (auto, auto), + [$0$], [exponent = 0 \ mantisse = 0], + [$plus.minus infinity$], [exponent = alle 1 \ mantisse = 0], + [NaN], [exponent = alle 1 \ mantisse > 0], + [denormalisierte Float], [exponent = 0 \ mantisse > 0], + [normalisierter Float], [0 < exponent < 255/2047] + ) ] #bgBlock(fill: colorProgramming)[ #subHeading(fill: colorProgramming)[C] + #table( + columns: (auto, auto, auto), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, + + [*C-Type*], [*min size*], [*typ. size*], + raw("char"), raw("1 byte"), raw("1 byte"), + raw("short (int)"), raw("2 byte"), raw("2 byte"), + raw("int"), raw("2 byte"), raw("4 byte"), + raw("long (int)"), raw("4 byte"), raw("8 byte"), + raw("long long"), raw("4 byte"), raw("8 byte"), + raw("float"), raw("4 byte"), raw("4 byte"), + raw("double"), raw("8 byte"), raw("8 byte"), + + ) + #table( columns: (auto, 1fr), fill: white, @@ -151,4 +278,99 @@ ] ) ] + + #bgBlock(fill: colorProgramming)[ + #subHeading(fill: colorProgramming)[#raw("scanf/printf") Format Specifier] + + #columns(2)[ + *printf* + #table( + columns: (auto, auto), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, + raw("%s"), [*String*], + raw("%d"), [*Decimal: #raw("int/short/long"))*], + raw("%f"), [*Float*], + raw("%f"), [*Float*], + raw("%lf"), [*Double*], + raw("%x"), [* Hexdecimal #raw("int/short/long")*], + ) + + Allgemeiner Syntax: #raw("%[flags][width][.precision]type") + + Flags: + - #raw("0") Prepend With left aligned + - #raw("-") Left-aligned + + #table(columns: (auto, auto), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, + raw("\\n"), [New Line], + raw("\\t"), [Tab], + raw("\\0"), [Null Terminator], + raw("\\\\"), [#raw("\\")], + raw("\\\""), [#raw("\"")], + ) + + #colbreak() + + *scanf* + #table( + columns: (auto, auto), + fill: (x, y) => if calc.rem(y, 2) == 0 { tableFillLow } else { tableFillHigh }, + raw("%[size of String]s"), [*String* \ Size of String (without the #raw("\\0")) \ Terminates with Whitespace], + raw("%i"), [*#raw("int")*], + raw("%f"), [*#raw("float")*], + raw("%lf"), [*#raw("double")*], + raw("%x"), [*#raw("int")* als Hexadezimal], + raw("%c"), [*#raw("char")* ], + ) + + #raw("fgets(char * s, int count, stdin)") + ] + ] + + #bgBlock(fill: colorMMIX)[ + #subHeading(fill: colorMMIX)[MMIX] + - $32$ Speziel Register + - $256$ Allzwickregister + - $2^64$ Speicher + + Wort: $64$ Bit + + ] + + #bgBlock(fill: colorRandomShit)[ + #subHeading(fill: colorRandomShit)[Register Register Magista] + + *Zwei-Address-Maschine:* $quad X <-- X dot.o Y$, Parameter: $(X,Y)$ \ + *Drei-Address-Maschine:* $quad X <-- Y dot.o Z$, Parameter: $(X,Y,Z)$ \ + *Ein-Address-Maschine:* $quad "ACC" <-- X$, Parameter: $(X)$ + + *Register-Speicher-Architekture:* \ + Operanden können Register und Addressen sein + + *Register-Register-Archiektur/Load-Store-Architektur* \ + Operanden nur Register. Extra Befehle fürs Laden aus Speicher + + + *CISC*: Complex Instruction Set Architecture + - Eine Befehl kann viel $->$ Wenige Befehle + - Befehlslänge Variable (meistens) + - z.B. x86 + + *RISC*: Reduced Instruction Set Architecture + - Eine Befehl kann wenig $->$ Viel Befehle + - Befehlslänge fix (meistens) + - z.B. 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b/src/lib/bit_fields.typ new file mode 100644 index 0000000..464aa7f --- /dev/null +++ b/src/lib/bit_fields.typ @@ -0,0 +1,40 @@ +#import "@preview/cetz:0.4.2" + +#let bitFieldField(name, color, total) = { + (name: name, color: color, total: total) +} + +#let bitFieldGreen = rgb("#8fff57") +#let bitFieldYellow = rgb("#ffe057") +#let bitFieldBlue = rgb("#57a5ff") +#let bitFieldRed = rgb("#ff5757") + +#let bitField(fields: (), BitHeight: 0.5, BitWidth: 0.25) = { + cetz.canvas({ + import cetz.draw : * + let pos = 0; + + let total = 0; + + for f in fields { + total += f.at("total") + } + + for f in fields { + content(((pos + 0.5)*BitWidth, -0.1), raw(str(total - pos - 1)), angle: 90deg, anchor: "east") + + for i in range(f.at("total")) { + rect(((pos + i)*BitWidth, 0), ((pos+i+1)*BitWidth, BitHeight), fill: f.at("color", default: bitFieldBlue)) + content(((pos+i+0.5)*BitWidth, BitHeight*0.5), raw("0")) + } + + content(((pos*BitWidth + f.at("total")*BitWidth*0.5), BitHeight + 0.2), f.at("name"), anchor: f.at("anchor", default: "mid")) + + pos += f.at("total") + + content(((pos - 0.5)*BitWidth, -0.1), raw(str(total - pos)), angle: 90deg, anchor: "east") + + } + }) +} +