[{"data":1,"prerenderedAt":1552},["ShallowReactive",2],{"content-\u002Ffaecher\u002Ftin\u002F3-4-zsmf-sa1":3},{"id":4,"title":5,"body":6,"class":1534,"description":1535,"extension":1536,"meta":1537,"navigation":1538,"path":1540,"pdfDownload":1541,"scope":1542,"scopeName":1543,"seo":1544,"stem":1545,"subject":1546,"subjectName":1547,"type":1548,"typeName":1549,"year":1550,"__hash__":1551},"faecher\u002Ffaecher\u002Ftin\u002F3-4-zsmf-sa1.md","Zusammenfassung – Schulaufgabe 1",{"type":7,"value":8,"toc":1487},"minimark",[9,14,22,27,45,50,55,64,69,72,76,79,101,104,107,131,137,141,145,150,153,156,163,167,180,183,186,191,194,198,212,216,220,225,231,298,301,305,308,316,320,327,330,333,337,341,343,356,358,361,375,381,385,396,400,403,463,466,469,472,478,481,484,488,491,494,499,503,529,533,603,607,642,646,654,658,669,672,677,681,689,693,710,713,718,722,730,751,756,771,775,780,784,789,793,798,807,811,839,843,868,872,876,884,889,893,904,908,912,943,947,960,963,966,969,973,984,987,990,998,1019,1024,1028,1038,1042,1070,1074,1085,1088,1098,1102,1110,1113,1115,1121,1137,1142,1146,1150,1185,1190,1194,1209,1213,1227,1231,1236,1240,1279,1282,1296,1299,1313,1317,1320,1372,1375,1378,1412,1415,1445,1448,1451],[10,11,13],"h1",{"id":12},"zahlensysteme","Zahlensysteme",[15,16,17,21],"p",{},[18,19,20],"strong",{},"Stellenwertsystem",": numerisches System, bei dem der Wert einer Ziffer durch ihre Position und die Basis des Systems bestimmt wird",[23,24,26],"h2",{"id":25},"binäres-zahlensystem","Binäres Zahlensystem",[28,29,30],"ul",{},[31,32,33,36,37],"li",{},[18,34,35],{},"Basis",": 2\n",[28,38,39,42],{},[31,40,41],{},"1 Bit: 2 Zustände (0 & 1)",[31,43,44],{},"8 Bit nennt man Oktett oder Byte",[46,47,49],"h3",{"id":48},"umrechnung","Umrechnung",[51,52,54],"h4",{"id":53},"binär-dezimal","Binär -> Dezimal",[56,57,58,61],"ol",{},[31,59,60],{},"Wert einer Stelle berechnen: Binärziffer * 2 Position der Binärziffer - 1",[31,62,63],{},"Werte addieren",[65,66,68],"h5",{"id":67},"beispiel","Beispiel",[15,70,71],{},"1101 -> (1 * 23) + (1 * 22) + (0 * 21) + (1 * 20) = 13",[51,73,75],{"id":74},"dezimal-binär","Dezimal -> Binär",[15,77,78],{},"Division mit ganzen Zahlen",[56,80,81,84,95,98],{},[31,82,83],{},"Division des Dezimalwertes durch 2",[31,85,86,87],{},"Rest aufschreiben\n",[56,88,89,92],{},[31,90,91],{},"Geht auf -> Rest: 0",[31,93,94],{},"Geht nicht auf -> Rest: 1",[31,96,97],{},"Wenn das Ergebnis nicht 0 ist, wieder bei 1. mit dem Ergebnis starten",[31,99,100],{},"Die Reste von unten nach oben ergeben die Binärzahl",[65,102,68],{"id":103},"beispiel-1",[15,105,106],{},"Dezimalzahl: 13",[56,108,109,115,121,126],{},[31,110,111,112],{},"13 \u002F 2 = 6 ",[18,113,114],{},"R: 1",[31,116,117,118],{},"6 \u002F 2 = 3 ",[18,119,120],{},"R: 0",[31,122,123,124],{},"3 \u002F 2 = 1 ",[18,125,114],{},[31,127,128,129],{},"1 \u002F 2 = 0 ",[18,130,114],{},[15,132,133,134],{},"13 -> ",[18,135,136],{},"1101",[46,138,140],{"id":139},"rechnungen","Rechnungen",[51,142,144],{"id":143},"addition","Addition",[28,146,147],{},[31,148,149],{},"Identisch zur schriftlichen Addition im Dezimalsystem",[65,151,68],{"id":152},"beispiel-2",[15,154,155],{},"1011 + 1110",[15,157,158],{},[159,160],"img",{"alt":161,"src":162},"","\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_1.png",[51,164,166],{"id":165},"multiplikation","Multiplikation",[28,168,169,172],{},[31,170,171],{},"Identisch zur schriftlichen Multiplikation im Dezimalsystem",[31,173,174,175],{},"Multiplikation ist komplexer als Addition\n",[28,176,177],{},[31,178,179],{},"Benötigt mehrere Taktzyklen",[65,181,68],{"id":182},"beispiel-3",[15,184,185],{},"101 * 11",[15,187,188],{},[159,189],{"alt":161,"src":190},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_2.png",[15,192,193],{},"101 * 11 = 1111",[65,195,197],{"id":196},"sonderfall-multiplikation-mit-2","Sonderfall: Multiplikation mit 2",[28,199,200,203,209],{},[31,201,202],{},"Bei einer Multiplikation mit 2 wird nur eine 0 angehängt",[31,204,205,206],{},"Fachbegriff für diese Aktion: ",[18,207,208],{},"Bitshift",[31,210,211],{},"Bitshift benötigt nur einen Taktzyklus",[51,213,215],{"id":214},"subtraktion","Subtraktion",[23,217,219],{"id":218},"hexadezimales-zahlensystem","Hexadezimales Zahlensystem",[15,221,222,224],{},[18,223,35],{},": 16",[15,226,227,230],{},[18,228,229],{},"Präfix",": 0x",[232,233,234,267],"table",{},[235,236,237],"thead",{},[238,239,240,246,249,252,255,258,261,264],"tr",{},[241,242,243],"th",{},[18,244,245],{},"Dezimal",[241,247,248],{},"0-9",[241,250,251],{},"10",[241,253,254],{},"11",[241,256,257],{},"12",[241,259,260],{},"13",[241,262,263],{},"14",[241,265,266],{},"15",[268,269,270],"tbody",{},[238,271,272,278,280,283,286,289,292,295],{},[273,274,275],"td",{},[18,276,277],{},"Hexadezimal",[273,279,248],{},[273,281,282],{},"A",[273,284,285],{},"B",[273,287,288],{},"C",[273,290,291],{},"D",[273,293,294],{},"E",[273,296,297],{},"F",[46,299,49],{"id":300},"umrechnung-1",[51,302,304],{"id":303},"hexadezimal-binär","Hexadezimal -> Binär",[15,306,307],{},"1 Hexadezimalziffer = 4 Binärstellen",[56,309,310,313],{},[31,311,312],{},"Hexadezimalziffern in je 4 Binärstellen umrechnen",[31,314,315],{},"Binärstellen aneinanderhängen",[51,317,319],{"id":318},"hexadezimal-dezimal","Hexadezimal -> Dezimal",[56,321,322,325],{},[31,323,324],{},"Wert einer Stelle berechnen: Dezimale Wertigkeit der Hexadezimalziffer * 16 Position der Binärziffer - 1",[31,326,63],{},[65,328,68],{"id":329},"beispiel-4",[15,331,332],{},"0xAFFE -> (10 * 163) + (15 * 162) + (15 * 161) + (14 * 160) = 45054",[51,334,336],{"id":335},"dezimal-hexadezimal","Dezimal -> Hexadezimal",[65,338,340],{"id":339},"möglichkeit-1-division-tr","Möglichkeit 1: Division (TR)",[15,342,78],{},[56,344,345,348,351,353],{},[31,346,347],{},"Division des Dezimalwertes durch 16",[31,349,350],{},"Rest aufschreiben",[31,352,97],{},[31,354,355],{},"Die Reste von unten nach oben ergeben die Hexadezimalzahl",[15,357,68],{},[15,359,360],{},"Dezimalzahl: 254",[56,362,363,369],{},[31,364,365,366],{},"254 \u002F 16 = 15 ",[18,367,368],{},"R: 14 -> E",[31,370,371,372],{},"15 \u002F 16 = 0 ",[18,373,374],{},"R: 15 -> F",[15,376,377,378],{},"254 -> ",[18,379,380],{},"0xFE",[65,382,384],{"id":383},"möglichkeit-2-über-binärsystem","Möglichkeit 2: Über Binärsystem",[28,386,387,390,393],{},[31,388,389],{},"Division durch 2 ist einfacher als durch 16",[31,391,392],{},"Binärergebnis in 4er Blöcke unterteilen",[31,394,395],{},"4er Blöcke in Hexadezimalzahl umrechnen",[397,398,68],"h6",{"id":399},"beispiel-5",[15,401,402],{},"Dezimalzahl: 3925",[56,404,405,410,415,420,425,430,435,440,445,450,455,459],{},[31,406,407,408],{},"3925 \u002F 2 = 1962 ",[18,409,114],{},[31,411,412,413],{},"1962 \u002F 2 = 981 ",[18,414,120],{},[31,416,417,418],{},"981 \u002F 2 = 490 ",[18,419,114],{},[31,421,422,423],{},"490 \u002F 2 = 245 ",[18,424,120],{},[31,426,427,428],{},"245 \u002F 2 = 122 ",[18,429,114],{},[31,431,432,433],{},"122 \u002F 2 = 61 ",[18,434,120],{},[31,436,437,438],{},"61 \u002F 2 = 30 ",[18,439,114],{},[31,441,442,443],{},"30 \u002F 2 = 15 ",[18,444,120],{},[31,446,447,448],{},"15 \u002F 2 = 7 ",[18,449,114],{},[31,451,452,453],{},"7 \u002F 2 = 3 ",[18,454,114],{},[31,456,123,457],{},[18,458,114],{},[31,460,128,461],{},[18,462,114],{},[15,464,465],{},"3925 -> 111101010101",[15,467,468],{},"1111 – 0101 – 0101",[15,470,471],{},"F 5 5",[15,473,474,475],{},"3925 -> ",[18,476,477],{},"0xF55",[46,479,140],{"id":480},"rechnungen-1",[51,482,144],{"id":483},"addition-1",[28,485,486],{},[31,487,149],{},[65,489,68],{"id":490},"beispiel-6",[15,492,493],{},"0xAFFE + 0x1111",[15,495,496],{},[159,497],{"alt":161,"src":498},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_3.png",[10,500,502],{"id":501},"binäre-logik","Binäre Logik",[28,504,505,511,517,523],{},[31,506,507,510],{},[18,508,509],{},"Binäre Variablen",": Nur zwei Zustände (0 & 1)",[31,512,513,516],{},[18,514,515],{},"Logiktabelle",": Enthält alle möglichen Kombinationen der Eingänge inklusive der entsprechenden Ausgänge",[31,518,519,522],{},[18,520,521],{},"Schaltfunktion",": Mathematischer Zusammenhang zwischen Eingang und Ausgang",[31,524,525,528],{},[18,526,527],{},"Logikblock",": Darstellung der logischen Verknüpfung der Variablen",[23,530,532],{"id":531},"grundfunktionen","Grundfunktionen",[232,534,535,557],{},[235,536,537],{},[238,538,539,544,548,553],{},[241,540,541],{},[18,542,543],{},"Name",[241,545,546],{},[18,547,515],{},[241,549,550],{},[18,551,552],{},"Funktion",[241,554,555],{},[18,556,527],{},[268,558,559,570,581,592],{},[238,560,561,564,566,568],{},[273,562,563],{},"Gleich",[273,565],{},[273,567],{},[273,569],{},[238,571,572,575,577,579],{},[273,573,574],{},"Nicht",[273,576],{},[273,578],{},[273,580],{},[238,582,583,586,588,590],{},[273,584,585],{},"Und",[273,587],{},[273,589],{},[273,591],{},[238,593,594,597,599,601],{},[273,595,596],{},"Oder",[273,598],{},[273,600],{},[273,602],{},[23,604,606],{"id":605},"abgeleitete-verknüpfungen","Abgeleitete Verknüpfungen",[232,608,609,629],{},[235,610,611],{},[238,612,613,617,621,625],{},[241,614,615],{},[18,616,543],{},[241,618,619],{},[18,620,515],{},[241,622,623],{},[18,624,552],{},[241,626,627],{},[18,628,527],{},[268,630,631],{},[238,632,633,636,638,640],{},[273,634,635],{},"Exklusives  Oder",[273,637],{},[273,639],{},[273,641],{},[23,643,645],{"id":644},"disjunktive-normalform-oder-normalform","Disjunktive Normalform (ODER-Normalform)",[28,647,648,651],{},[31,649,650],{},"Spezielle Form einer logischen Formel",[31,652,653],{},"Besteht aus beliebig vielen Konjunktionen (UND) verknüpft durch Disjunktionen (ODER)",[46,655,657],{"id":656},"bildung-einer-dnf-aus-einer-wertetabelle","Bildung einer DNF aus einer Wertetabelle",[56,659,660,663,666],{},[31,661,662],{},"Alle wahren Zeilen finden",[31,664,665],{},"Konjunktion für jede wahre Zeile erstellen",[31,667,668],{},"Jede erstellte Konjunktion mit einem ODER verknüpfen",[46,670,68],{"id":671},"beispiel-7",[28,673,674],{},[31,675,676],{},"Drei Konjunktionen verbunden durch zwei ODER-Verknüpfungen",[23,678,680],{"id":679},"kv-diagramm","KV-Diagramm",[28,682,683,686],{},[31,684,685],{},"Diagramm um die minimalste Formel einer Schaltung zu ermitteln",[31,687,688],{},"Anzahl der Zellen: 2 Anzahl der Eingangsvariablen",[46,690,692],{"id":691},"minimalisierung-mit-einem-kv-diagramm-aus-einer-wertetabelle","Minimalisierung mit einem KV-Diagramm aus einer Wertetabelle",[56,694,695,698,701,704,707],{},[31,696,697],{},"Übertragen der 1-Zustände in das KV-Diagramm",[31,699,700],{},"Rest mit 0-Zuständen auffüllen",[31,702,703],{},"Alle benachbarten Zellen umranden (auch über die Kanten des Diagramms hinaus auf die andere Seite)",[31,705,706],{},"Einzelne Blöcke bestehen nur noch aus Variablen, die sich innerhalb des Blockes nicht verändern",[31,708,709],{},"Blöcke mit ODER-Verknüpfungen miteinander verbinden",[51,711,68],{"id":712},"beispiel-8",[15,714,715],{},[159,716],{"alt":161,"src":717},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_9.png",[10,719,721],{"id":720},"volladdierer","Volladdierer",[28,723,724,727],{},[31,725,726],{},"Addieren mit binären Operationen",[31,728,729],{},"3 Eingänge notwendig",[56,731,732,739,745],{},[31,733,734,735,738],{},"Erster Summand (",[18,736,737],{},"x",")",[31,740,741,742,738],{},"Zweiter Summand (",[18,743,744],{},"y",[31,746,747,748,738],{},"Carry – In: Übertrag von vorherigem Durchgang (",[18,749,750],{},"Cin",[28,752,753],{},[31,754,755],{},"2 Ausgänge",[56,757,758,764],{},[31,759,760,761,738],{},"Summe aus erstem und zweitem Summanden (",[18,762,763],{},"s",[31,765,766,767,770],{},"Carry – Out: Übertrag aus der Summe (",[18,768,769],{},"Cout",") -> wird Carry – In",[23,772,774],{"id":773},"schaltung-eines-volladierers","Schaltung eines Volladierers",[15,776,777],{},[159,778],{"alt":161,"src":779},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_10.png",[23,781,783],{"id":782},"wahrheitstabelle-eines-volladdierers","Wahrheitstabelle eines Volladdierers",[15,785,786],{},[159,787],{"alt":161,"src":788},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_11.png",[23,790,792],{"id":791},"schaltung-eines-halbaddierers","Schaltung eines Halbaddierers",[15,794,795],{},[159,796],{"alt":161,"src":797},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_12.png",[15,799,800,801],{},"Quelle: ",[802,803,804],"a",{"href":804,"rel":805},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=Od-9-vIJapo",[806],"nofollow",[10,808,810],{"id":809},"multiplexer","Multiplexer",[28,812,813,816,819,822],{},[31,814,815],{},"Digitale Schaltung",[31,817,818],{},"Mehrere Eingangssignale auf einen Ausgang",[31,820,821],{},"Über Steuerleitungen wird entschieden welcher Eingang gewählt wird",[31,823,824,825],{},"Typen:\n",[28,826,827,833],{},[31,828,829,832],{},[18,830,831],{},"N-zu-1 Multiplexer",": Wählt eines von N Eingangssignalen aus",[31,834,835,838],{},[18,836,837],{},"1-zu-N Demultiplexer",": Verteilt einen Ausgang auf einen von N Ausgängen",[23,840,842],{"id":841},"anwendungen","Anwendungen",[28,844,845,856,862],{},[31,846,847,850,851],{},[18,848,849],{},"Datenübertragung",": Telekommunikation verwendet Multiplexer, um mehrere Datenströme über eine Leitung zu übertragen\n",[28,852,853],{},[31,854,855],{},"Erhöht Effizienz",[31,857,858,861],{},[18,859,860],{},"Schaltnetzwerke",": Multiplexer ermöglichen das Routing in Schaltnetzwerken",[31,863,864,867],{},[18,865,866],{},"Adressierung in Speichern",": Zur Auswahl des richtigen Speicherorts in Speicheradressierungssystemen",[23,869,871],{"id":870},"beispiele","Beispiele",[46,873,875],{"id":874},"_1-mux","1-Mux",[15,877,878,881],{},[159,879],{"alt":161,"src":880},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_13.png",[159,882],{"alt":161,"src":883},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_14.png",[15,885,886],{},[159,887],{"alt":161,"src":888},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_15.png",[46,890,892],{"id":891},"_2-mux","2-Mux",[15,894,895,898,901],{},[159,896],{"alt":161,"src":897},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_16.png",[159,899],{"alt":161,"src":900},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_17.png",[159,902],{"alt":161,"src":903},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_18.png",[10,905,907],{"id":906},"darstellung-negativer-zahlen","Darstellung negativer Zahlen",[23,909,911],{"id":910},"einerkomplement","Einerkomplement",[28,913,914,917,926,937,940],{},[31,915,916],{},"Veralteter Standard",[31,918,919,922,923],{},[18,920,921],{},"MSB",": Most Significant Bit -> ",[18,924,925],{},"Das linkeste Bit",[31,927,928,929],{},"MSB wird verwendet um das Vorzeichen zu wählen\n",[28,930,931,934],{},[31,932,933],{},"0: Positiv",[31,935,936],{},"1: Negativ",[31,938,939],{},"Größte Positive Zahl: 2Anzahl Bits – 1 – 1",[31,941,942],{},"Größte Negative Zahl: -2Anzahl Bits – 1 – 1",[46,944,946],{"id":945},"bildung-des-einerkomplements","Bildung des Einerkomplements",[28,948,949],{},[31,950,951,952],{},"Alle Bits einer Binärzahl invertieren\n",[28,953,954,957],{},[31,955,956],{},"Aus 0 wird 1",[31,958,959],{},"Aus 1 wird 0",[51,961,68],{"id":962},"beispiel-9",[15,964,965],{},"Binärzahl: 010110",[15,967,968],{},"Einerkomplement der Binärzahl: 101001",[46,970,972],{"id":971},"subtraktion-mit-dem-einerkomplement","Subtraktion mit dem Einerkomplement",[56,974,975,978,981],{},[31,976,977],{},"Subtrahend invertieren um das Vorzeichen zu setzen",[31,979,980],{},"Minuend und invertierten Subtrahend addieren",[31,982,983],{},"Bei einem Überlauf, den Überlauf zum Ergebnis addieren",[51,985,68],{"id":986},"beispiel-10",[15,988,989],{},"4-3",[28,991,992,995],{},[31,993,994],{},"4: 0100",[31,996,997],{},"3: 0011",[56,999,1000,1008,1011],{},[31,1001,1002,1003],{},"Subtrahend Invertieren\n",[56,1004,1005],{},[31,1006,1007],{},"0011 -> 1100",[31,1009,1010],{},"0100 + 1100 = 1 0000",[31,1012,1013,1014],{},"Überlauf addieren\n",[56,1015,1016],{},[31,1017,1018],{},"0000 + 0001 = 0001",[28,1020,1021],{},[31,1022,1023],{},"Ergebnis: 1",[51,1025,1027],{"id":1026},"problem","Problem",[28,1029,1030],{},[31,1031,1032,1033],{},"Wenn es einen Übertritt über 0 gibt\n",[28,1034,1035],{},[31,1036,1037],{},"Z.B. 6-4",[23,1039,1041],{"id":1040},"zweierkomplement","Zweierkomplement",[28,1043,1044,1047,1050,1057,1065,1067],{},[31,1045,1046],{},"Einheitliche Darstellung",[31,1048,1049],{},"Löst einige Probleme des Einerkomplements",[31,1051,1052,922,1054],{},[18,1053,921],{},[18,1055,1056],{},"das linkeste Bit",[31,1058,928,1059],{},[28,1060,1061,1063],{},[31,1062,933],{},[31,1064,936],{},[31,1066,939],{},[31,1068,1069],{},"Größte Negative Zahl: -2Anzahl Bits – 1",[46,1071,1073],{"id":1072},"bildung-des-zweierkomplements","Bildung des Zweierkomplements",[56,1075,1076,1079,1082],{},[31,1077,1078],{},"Binärzahl ermitteln",[31,1080,1081],{},"Einerkomplement bilden",[31,1083,1084],{},"1 zum Einerkomplement addieren",[51,1086,68],{"id":1087},"beispiel-11",[56,1089,1090,1092,1095],{},[31,1091,965],{},[31,1093,1094],{},"Einerkomplement: 010110 -> 101001",[31,1096,1097],{},"1 Addieren: 101001 + 1 = 101010",[46,1099,1101],{"id":1100},"subtraktion-mit-dem-zweierkomplement","Subtraktion mit dem Zweierkomplement",[56,1103,1104,1107],{},[31,1105,1106],{},"Zweierkomplement vom Subtrahend bilden",[31,1108,1109],{},"Minuend und Subtrahend addieren",[51,1111,68],{"id":1112},"beispiel-12",[15,1114,989],{},[28,1116,1117,1119],{},[31,1118,994],{},[31,1120,997],{},[56,1122,1123,1134],{},[31,1124,1125,1126],{},"Zweierkomplement bilden\n",[56,1127,1128,1131],{},[31,1129,1130],{},"Einerkomplement bilden: 0011 -> 1100",[31,1132,1133],{},"1 Addieren: 1100 + 1 = 1101",[31,1135,1136],{},"Addieren: 0100 + 1101 = 1 0001",[28,1138,1139],{},[31,1140,1141],{},"Übertrag entfällt, da nur 4 Bit",[10,1143,1145],{"id":1144},"rationale-zahlen","Rationale Zahlen",[23,1147,1149],{"id":1148},"festkommaarithmetik","Festkommaarithmetik",[28,1151,1152,1168,1171,1174],{},[31,1153,1154,1155],{},"Position des Kommas ist vorgegeben\n",[28,1156,1157],{},[31,1158,1159,1160],{},"Beispiel (8Bit)\n",[28,1161,1162,1165],{},[31,1163,1164],{},"4-Bits vor dem Komma",[31,1166,1167],{},"4-Bits nach dem Komma",[31,1169,1170],{},"Begrenzte Genauigkeit durch feste Kommaposition",[31,1172,1173],{},"Grundrechenarten sind ähnlich wie bei Dezimalzahlen",[31,1175,1176,1177],{},"Anwendung in:\n",[28,1178,1179,1182],{},[31,1180,1181],{},"Eingebetteten Systemen",[31,1183,1184],{},"Anwendungen bei denen eine feste Anzahl von Bits vor\u002Fnach dem Komma erforderlich ist (Bildverarbeitung)",[15,1186,1187],{},[159,1188],{"alt":161,"src":1189},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_19.png",[46,1191,1193],{"id":1192},"vorteile","Vorteile",[28,1195,1196],{},[31,1197,1198,1201],{},[18,1199,1200],{},"Einfachheit",[28,1202,1203,1206],{},[31,1204,1205],{},"Erfordert weniger komplexe Hardware",[31,1207,1208],{},"Kann effizienter implementieret werden+",[46,1210,1212],{"id":1211},"nachteile","Nachteile",[28,1214,1215,1221],{},[31,1216,1217,1220],{},[18,1218,1219],{},"Begrenzte Dynamik",": Sehr große oder sehr kleine Werte werden ggf. ungenau",[31,1222,1223,1226],{},[18,1224,1225],{},"Genauigkeitsverlust",": Berechnung mit komplexen Zahlen kann zu Rundungsfehlern führen",[46,1228,1230],{"id":1229},"beispiel-für-addition","Beispiel für Addition",[15,1232,1233],{},[159,1234],{"alt":161,"src":1235},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_20.png",[23,1237,1239],{"id":1238},"fließkommaarithmetik","Fließkommaarithmetik",[28,1241,1242,1245,1265,1273,1276],{},[31,1243,1244],{},"Komma kann verschoben werden",[31,1246,1247,1248],{},"Bestandteile:\n",[28,1249,1250,1255,1260],{},[31,1251,1252],{},[18,1253,1254],{},"1 Bit: Vorzeichen",[31,1256,1257],{},[18,1258,1259],{},"8 Bit: Exponent",[31,1261,1262],{},[18,1263,1264],{},"23 Bit: Mantisse",[31,1266,1267,1268],{},"Innerhalb der Mantisse lässt sich das Komma verschieben\n",[28,1269,1270],{},[31,1271,1272],{},"Große und kleine Zahlen mit unterschiedlicher Genauigkeit",[31,1274,1275],{},"Hohe Dynamik und Genauigkeit",[31,1277,1278],{},"Erfordert spezielle Algorithmen um den Exponenten und die Mantisse festzulegen",[46,1280,1193],{"id":1281},"vorteile-1",[28,1283,1284,1290],{},[31,1285,1286,1289],{},[18,1287,1288],{},"Hohe Genauigkeit und Dynamik",": Breiter Bereich von Zahlen mit unterschiedlicher Genauigkeit",[31,1291,1292,1295],{},[18,1293,1294],{},"Flexibilität",": Durch das Verschieben des Kommas",[46,1297,1212],{"id":1298},"nachteile-1",[28,1300,1301,1307],{},[31,1302,1303,1306],{},[18,1304,1305],{},"Komplexität",": Erfordert komplexe Algorithmen und Hardware",[31,1308,1309,1312],{},[18,1310,1311],{},"Rundungsfehler",": Bei komplexen Berechnungen oder Darstellung von Zahlen die nicht in das Gleitkommazahlenformat passen",[46,1314,1316],{"id":1315},"berechnung-einer-gleitkommazahl","Berechnung einer Gleitkommazahl",[51,1318,75],{"id":1319},"dezimal-binär-1",[56,1321,1322,1333,1336,1339,1342,1353,1364],{},[31,1323,1324,1325],{},"Vorzeichenbit festlegen\n",[56,1326,1327,1330],{},[31,1328,1329],{},"Positiv: 0",[31,1331,1332],{},"Negativ: 1",[31,1334,1335],{},"Vorkommazahl umrechnen",[31,1337,1338],{},"Nachkommazahl umrechnen",[31,1340,1341],{},"Gesamtzahl bilden durch Verkettung von Vor- & Nachkommazahl",[31,1343,1344,1345],{},"Normieren: Es darf & muss nur eine 1 vor dem Komma stehen\n",[56,1346,1347,1350],{},[31,1348,1349],{},"Verschiebung durch 2 Stellen um die Verschoben wird",[31,1351,1352],{},"Alles nach dem Komma ist die Mantisse",[31,1354,1355,1356],{},"Exponent umrechnen: Verschobene Stellen + 127 = Exponent\n",[56,1357,1358,1361],{},[31,1359,1360],{},"Verschobene Stellen können ggf. auch negativ sein",[31,1362,1363],{},"In Binär umrechnen",[31,1365,1366,1367],{},"Vorzeichen, Exponent und Mantisse in dieser Reihenfolge verketten\n",[56,1368,1369],{},[31,1370,1371],{},"Rest mit 0en auffüllen",[65,1373,68],{"id":1374},"beispiel-13",[15,1376,1377],{},"Ausgangszahl: 18,4",[56,1379,1380,1383,1386,1392,1395,1406,1409],{},[31,1381,1382],{},"Vorzeichen: Positiv -> 0",[31,1384,1385],{},"Vorkommazahl: 18 -> 10010",[31,1387,1388,1391],{},[159,1389],{"alt":161,"src":1390},"\u002Fdownloads\u002FTIN\u002Fimages\u002F3-4-zsmf-sa1_img_21.png","Nachkommazahl umrechnen: 0,4 -> 0110",[31,1393,1394],{},"Gesamtzahl bilden: 10010,0110",[31,1396,1397,1398],{},"Normieren: Komma muss um 4 Stellen verschoben werden\n",[56,1399,1400,1403],{},[31,1401,1402],{},"10010,0110 = 1,00100110 * 24",[31,1404,1405],{},"Mantisse: 00100110",[31,1407,1408],{},"Exponent bestimmen: 4 + 127 = 131 -> 10000011",[31,1410,1411],{},"Verketten und 0en auffüllen: 0 10000011 00100110 000000000000000",[51,1413,54],{"id":1414},"binär-dezimal-1",[56,1416,1417,1420,1423,1431,1439,1442],{},[31,1418,1419],{},"Einteilung in Vorzeichenbit, Exponent und Mantisse",[31,1421,1422],{},"Vorzeichen merken",[31,1424,1425,1426],{},"Exponentenbereich in Dezimal umrechnen\n",[56,1427,1428],{},[31,1429,1430],{},"Dezimalzahl – 127 = Exponent",[31,1432,1433,1434],{},"Komma der Mantisse entsprechend verschieben\n",[56,1435,1436],{},[31,1437,1438],{},"Führende 1 vor dem Komma behalten!",[31,1440,1441],{},"Vor- & Nachkommazahl in Dezimalumrechnen und verketten",[31,1443,1444],{},"Vorzeichen setzen",[65,1446,68],{"id":1447},"beispiel-14",[15,1449,1450],{},"Ausgangszahl: 10111111000000000000000000000000",[56,1452,1453,1456,1459,1467,1470,1481,1484],{},[31,1454,1455],{},"Einteilen: 1-01111110-00000000000000000000000",[31,1457,1458],{},"Vorzeichen: 1 -> -",[31,1460,1461,1462],{},"Exponent in Dezimal: 126\n",[56,1463,1464],{},[31,1465,1466],{},"126 – 127 = -1",[31,1468,1469],{},"Komma der Mantisse verschieben: 1,0 -> 0,1",[31,1471,1472,1473],{},"In Dezimal umrechnen\n",[56,1474,1475,1478],{},[31,1476,1477],{},"Vorkomma: 0 -> 0",[31,1479,1480],{},"Nachkomma: 1 -> ,5",[31,1482,1483],{},"Verketten: 0,5",[31,1485,1486],{},"Vorzeichen setzen: -0,5",{"title":161,"searchDepth":1488,"depth":1488,"links":1489},2,[1490,1495,1499,1500,1501,1505,1508,1509,1510,1511,1512,1516,1520,1524,1529],{"id":25,"depth":1488,"text":26,"children":1491},[1492,1494],{"id":48,"depth":1493,"text":49},3,{"id":139,"depth":1493,"text":140},{"id":218,"depth":1488,"text":219,"children":1496},[1497,1498],{"id":300,"depth":1493,"text":49},{"id":480,"depth":1493,"text":140},{"id":531,"depth":1488,"text":532},{"id":605,"depth":1488,"text":606},{"id":644,"depth":1488,"text":645,"children":1502},[1503,1504],{"id":656,"depth":1493,"text":657},{"id":671,"depth":1493,"text":68},{"id":679,"depth":1488,"text":680,"children":1506},[1507],{"id":691,"depth":1493,"text":692},{"id":773,"depth":1488,"text":774},{"id":782,"depth":1488,"text":783},{"id":791,"depth":1488,"text":792},{"id":841,"depth":1488,"text":842},{"id":870,"depth":1488,"text":871,"children":1513},[1514,1515],{"id":874,"depth":1493,"text":875},{"id":891,"depth":1493,"text":892},{"id":910,"depth":1488,"text":911,"children":1517},[1518,1519],{"id":945,"depth":1493,"text":946},{"id":971,"depth":1493,"text":972},{"id":1040,"depth":1488,"text":1041,"children":1521},[1522,1523],{"id":1072,"depth":1493,"text":1073},{"id":1100,"depth":1493,"text":1101},{"id":1148,"depth":1488,"text":1149,"children":1525},[1526,1527,1528],{"id":1192,"depth":1493,"text":1193},{"id":1211,"depth":1493,"text":1212},{"id":1229,"depth":1493,"text":1230},{"id":1238,"depth":1488,"text":1239,"children":1530},[1531,1532,1533],{"id":1281,"depth":1493,"text":1193},{"id":1298,"depth":1493,"text":1212},{"id":1315,"depth":1493,"text":1316},"3-4","Stellenwertsystem: numerisches System, bei dem der Wert einer Ziffer durch ihre Position und die Basis des Systems bestimmt wird","md",{},{"title":1539},"Zusammenfassung – Schulaufgabe 1 (2023\u002F2024)","\u002Ffaecher\u002Ftin\u002F3-4-zsmf-sa1","\u002Fdownloads\u002FTIN\u002FTIN_3-4_ZSMF_SA1.pdf","SA1","Schulaufgabe 1",{"title":5,"description":1535},"faecher\u002Ftin\u002F3-4-zsmf-sa1","TIN","Technische Informatik","ZSMF","Zusammenfassung","2023\u002F2024","Z2eLyPNi-vwaWUfWISLg98fWPyBkd8gCHS_QWqQE4Ag",1778676320875]