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Martin Admek (UHK-FIM-KIT)O  =F .PRIPO Principy po ta o$P3.11.2009  cvi en . 7 Logick funkce $)'*Organiza n drobnosti dochzka F  $f:Binrn (booleovsk) promnn(<jedna slice dvojkov soustavy pravda x nepravda, true x false, 1 x 0 v praxi napY. 5V x 0V pYi programovn typ Bool(ean) George Boole (obrzek z Wikipedie)<| |  t33Logick opertory (funkce)VLogick sou in (a zroveH, AND) Y=A*B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vaechny vstupy=1 (stejn jako aritmetick sou in) Logick sou et (nebo, OR) Y=A+B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt alespoH jeden vstup=1 (1+1=1; nezamHujte s aritmetickm sou tem) )H)X )H  )XLogick opertory (funkce)Negace (inverze, NOT) Y= zmna 0-1 a naopak Vlu n nebo (exclusive OR, XOR) Y = A XOR B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vstupy rozn (prv jeden vstup je 1) odpovd spojce  , nebo s rkou bu, anebo  ale ne oba!/#$" "  "  "  "##$  $$("(: #  Logick opertory (funkce)NAND (Schefferova fce) negace sou inu (NOT AND) tabulka pro A,B,C,Y... ...Y=1, pokud alespoH 1 vstup nen 1 NOR (Piercova fce) negace sou tu (NOT AND) tabulka pro A,B,C,Y... ...Y=1, pokud ~dn vstup nen 1pUP<    "P \R Logick opertory (funkce)&Dala: ekvivalence (rovnost) a=b y=a*b+anon*bnon antivalence (neekvivalence) inhibice (pYm, zptn) 1 ze 2 variant XORu implikace (pYm, zptn)5     n'  * Logick opertory (funkce)(napY. pYi programovn) mo~n pou~it na sla>1 (ne booleovsk) provd se samostatn po jednotlivch bitech napY. logick sou in x=5&6; //syntaxe C-like jazyko ... = 0101b & 0110b = 0100b = 4d napY. logick sou et 5|6= ? ... = 0101b | 0110b = 0111b = 7d => v pYpad logickch (nikoliv aritmetickch) opertoro tedy 5x6=4 5+6=7BZBZ@ZZ(Z>Z ZB"B")"*"*"*"*" " "*"*"*"*>" "v  *  ^ NGrafick zznam logickch fc/opertoro((( #AND (&), OR (1), NOT (o), NAND, NOR !Booleova algebra vizte pYednaku .5 komutativn, asociativn, distributivn a dala zkony&77"pln soubor logickch funkcrumo~Huje realizovat jakoukoliv logickou fci. 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Martin Admek631Microsoft Office PowerPoint@s\@WS,@p:^E]rGhg  ,V'&" WMFC <8IDAT1W}{{J %s4!u61QJuRW&x&vxIENDB` ne!(mPɈPNG  IHDRysRGBPLTEffffffff̙̙O) cmPPJCmp0712 jtRNS ADIDATcP, SVA%6AC!P.iuD!".l`)SbPbL@]KIENDB`T#<?v, bPRIPO, cvi en  Ing. Martin Admek (UHK-FIM-KIT)O  =" .PRIPO Principy po ta o$P3.11.2009  cvi en . 7 Logick funkce $)'*Organiza n drobnosti dochzka F  $f:Binrn (booleovsk) promnn(<jedna slice dvojkov soustavy pravda x nepravda, true x false, 1 x 0 v praxi napY. 5V x 0V pYi programovn typ Bool(ean) George Boole (obrzek z Wikipedie)<| |  t33Logick opertory (funkce)VLogick sou in (a zroveH, AND) Y=A*B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vaechny vstupy=1 (stejn jako aritmetick sou in) Logick sou et (nebo, OR) Y=A+B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt alespoH jeden vstup=1 (1+1=1; nezamHujte s aritmetickm sou tem) )H)X )H  )XLogick opertory (funkce)Negace (inverze, NOT) Y= zmna 0-1 a naopak Vlu n nebo (exclusive OR, XOR) Y = A XOR B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vstupy rozn (prv jeden vstup je 1) odpovd spojce  , nebo s rkou bu, anebo  ale ne oba!/#$" "  "  "  "##$  $$("(: #  Logick opertory (funkce)NAND (Schefferova fce) negace sou inu (NOT AND) tabulka pro A,B,C,Y... ...Y=1, pokud alespoH 1 vstup nen 1 NOR (Piercova fce) negace sou tu (NOT AND) tabulka pro A,B,C,Y... ...Y=1, pokud ~dn vstup nen 1pUP<    "P \R Logick opertory (funkce)&Dala: ekvivalence (rovnost) a=b y=a*b+anon*bnon antivalence (neekvivalence) inhibice (pYm, zptn) 1 ze 2 variant XORu implikace (pYm, zptn)5     n'  * Logick opertory (funkce)(napY. pYi programovn) mo~n pou~it na sla>1 (ne booleovsk) provd se samostatn po jednotlivch bitech napY. logick sou in x=5&6; //syntaxe C-like jazyko ... = 0101b & 0110b = 0100b = 4d napY. logick sou et 5|6= ? ... = 0101b | 0110b = 0111b = 7d => v pYpad logickch (nikoliv aritmetickch) o  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_abcdefghijklmnopqrstuvwxyz{|}~E      !"#$%&'()*+,-./123456789:;<=>?aDFGHIJKLMNOPQRSTUVWXYZ[\]0`bcdefghijklmnopqrstuvwxz{|}~Root EntrydO)`^E]_PicturesCurrent UserVSummaryInformation(PowerPoint Document(` DocumentSummaryInformation8dDArialngsRomanll O 0"DTimes New Romanll O 0 DWingdingsRomanll O 0@ . @n?" dd@  @@`` ` / /))*-+E\]hi/X$b$jsn 0AA @8  "Q ʚ;y8ʚ;g4YdYd O 0,ppp@ <4dddd8v 0l  <4!d!d8 0lg4SdSdP O 08p@ pp<4BdBd8v 0l 00___PPT10 pp___PPT9n3n)/ypf}I[ePNG  IHDR asRGB`PLTEkjjjUU@@@??@??+++**+**#g cmPPJCmp07128I tRNS@fAIDAT 0 ~{[8([Pz2S82(\dXP< zIENDB`0n&WvlHMU+vnPNG  IHDR asRGB`PLTEkjjkjjUUTU@@@??@++*+**M#A cmPPJCmp07128I tRNS@f>IDAT1W}{{J %s4!u61QJuRW&x&vxIENDB` ne!(mPɈPNG  IHDRysRGBPLTEffffffff̙̙O) cmPPJCmp0712 jtRNS ADIDATcP, SVA%6AC!P.iuD!".l`)SbPbL@]KIENDB`T#<?v, bPRIPO, cvi en  Ing. Martin Admek (UHK-FIM-KIT)O  =" .PRIPO Principy po ta o$P3.11.2009  cvi en . 7 Logick funkce $)'*Organiza n drobnosti dochzka F  $f:Binrn (booleovsk) promnn(<jedna slice dvojkov soustavy pravda x nepravda, true x false, 1 x 0 v praxi napY. 5V x 0V pYi programovn typ Bool(ean) George Boole (obrzek z Wikipedie)<| |  t33Logick opertory (funkce)VLogick sou in (a zroveH, AND) Y=A*B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vaechny vstupy=1 (stejn jako aritmetick sou in) Logick sou et (nebo, OR) Y=A+B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt alespoH jeden vstup=1 (1+1=1; nezamHujte s aritmetickm sou tem) )H)X )H  )XLogick opertory (funkce)Negace (inverze, NOT) Y= zmna 0-1 a naopak Vlu n nebo (exclusive OR, XOR) Y = A XOR B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vstupy rozn (prv jeden vstup je 1) odpovd spojce  , nebo s rkou bu, anebo  ale ne oba!/#$" "  "  "  "##$  $$("(: #  Logick opertory (funkce)NAND (Schefferova fce) negace sou inu (NOT AND) tabulka pro A,B,C,Y... ...Y=1, pokud alespoH 1 vstup nen 1 NOR (Piercova fce) negace sou tu (NOT AND) tabulka pro A,B,C,Y... ...Y=1, pokud ~dn vstup nen 1pUP<    "P \R Logick opertory (funkce)&Dala: ekvivalence (rovnost) a=b y=a*b+anon*bnon antivalence (neekvivalence) inhibice (pYm, zptn) 1 ze 2 variant XORu implikace (pYm, zptn)5     n'  * Logick opertory (funkce)(napY. pYi programovn) mo~n pou~it na sla>1 (ne booleovsk) provd se samostatn po jednotlivch bitech napY. logick sou in x=5&6; //syntaxe C-like jazyko ... = 0101b & 0110b = 0100b = 4d napY. logick sou et 5|6= ? ... = 0101b | 0110b = 0111b = 7d => v pYpad logickch (nikoliv aritmetickch) opertoro tedy 5x6=4 5+6=7BZBZ@ZZ(Z>Z ZB"B")"*"*"*"*" " "*"*"*"*>" "v  *  ^ NGrafick zznam logickch fc/opertoro((( #AND (&), OR (1), NOT (o), NAND, NOR !Booleova algebra vizte pYednaku .5 komutativn, asociativn, distributivn a dala zkony&77"pln soubor logickch funkcrumo~Huje realizovat jakoukoliv logickou fci. (jakoukoliv kombinaci vstupo a vstupu) OR, AND, NOT pro n definovna Booleova algebra existuj dala pl. soubory l.f., ale nepou~vaj seLb#5 D#5>(I##Zpis logick fce"pravdivostn tabulka (vstupy, vstupy) algebraick vraz mapa (pYat) PY: napiate pravdivostn tabulky pro vrazy y=(a*b)+c y=(a+b)*c y=(*b)+cBGlZKlZ .HA Z PYatDe Morganovy vztahy / zkony pYevod mezi sou inem a sou tem vysvtlen NOR a NAND realizovatelnost NOT, AND, OR jednm typem sou stky (nkolikerm pou~itm jedn fce) Karnaughovy mapy nzorn grafick 2D zobrazen, pYepis tabulky do algeb.vrazu nalezen podobnch kombinac, kter vedou ke stejnmu vsledku zjednoduaen logick funkce^ZZZZ  P  7c/l[g !"#rs !1.0( / 0DArialngsRomanll O 0"DTimes New Romanll O 0 DWingdingsRomanll O 0@ . @n?" dd@  @@`` ՜.+,04    Pedvdn na obrazovceNchod a  ' ArialTimes New Roman WingdingsPaprskyPRIPO Principy potaOrganizan drobnostiBinrn (booleovsk) promnnLogick opertory (funkce)Logick opertory (funkce)Logick opertory (funkce)Logick opertory (funkce)Logick opertory (funkce)(Grafick zznam logickch fc/opertorBooleova algebrapln soubor logickch funkcZpis logick fcePt Pouit psmaablona nvrhuNadpisy snmk *_Ing. Martin AdmekIng. Martin Admekpertoro tedy 5x6=4 5+6=7BZBZ@ZZ(Z>Z ZB"B")"*"*"*"*" " "*"*"*"*>" "v  *  ^ NGrafick zznam logickch fc/opertoro((( #AND (&), OR (1), NOT (o), NAND, NOR !Booleova algebra vizte pYednaku .5 komutativn, asociativn, distributivn a dala zkony&77"pln soubor logickch funkcrumo~Huje realizovat jakoukoliv logickou fci. (jakoukoliv kombinaci vstupo a vstupu) OR, AND, NOT pro n definovna Booleova algebra existuj dala pl. soubory l.f., ale nepou~vaj seLb#5 D#5>(I##Zpis logick fce"pravdivostn tabulka (vstupy, vstupy) algebraick vraz mapa (pYat) PY: napiate pravdivostn tabulky pro vrazy y=(a*b)+c y=(a+b)*c y=(*b)+cBGlZKlZ .HA Z PYatDe Morganovy vztahy / zkony pYevod mezi sou inem a sou tem vysvtlen NOR a NAND realizovatelnost NOT, AND, OR jednm typem sou stky (nkolikerm pou~itm jedn fce) Karnaughovy mapy nzorn grafick 2D zobrazen, pYepis tabulky do algeb.vrazu nalezen podobnch kombinac, kter vedou ke stejnmu vsledku zjednoduaen logick funkce^ZZZZ  P  7c/l[g !"#r"s !JR10( / 0DArialngsRomanllyO 0DTimes New RomanllyO 0 DWingdingsRomanllyO 0@ . @n?" dd@  @@`` ` / /))*-+E\]hi/X$b$jsn 0AA @8  $Q ʚ;y8ʚ;g4jdjd O 0ppp@ <4dddd8v 0lpy <4!d!d8 0lg4SdSd O 08p@ pp<4BdBd8v 0lpy20___PPT10 pp___PPT9n3n)/ypf}I[ePNG  IHDR asRGB`PLTEkjjjUU@@@??@??+++**+**#g cmPPJCmp07128I tRNS@fAIDAT 0 ~{[8([Pz2S82(\dXP< zIENDB`0n&WvlHMU+vnPNG  IHDR asRGB`PLTEkjjkjjUUTU@@@??@++*+**M#A cmPPJCmp07128I tRNS@f>IDAT1W}{{J %s4!u61QJuRW&x&vxIENDB` ne!(mPɈPNG  IHDRysRGBPLTEffffffff̙̙O) cmPPJCmp0712 jtRNS ADIDATcP, SVA%6AC!P.iuD!".l`)SbPbL@]KIENDB`V#>?v, bPRIPO, cvi en  Ing. Martin Admek (UHK-FIM-KIT)O  =z .PRIPO Principy po ta o$P3.11.2009  cvi en . 7 Logick funkce $)'*Organiza n drobnosti dochzka F  $f:Binrn (booleovsk) promnn(<jedna slice dvojkov soustavy pravda x nepravda, true x false, 1 x 0 v praxi napY. 5V x 0V pYi programovn typ Bool(ean) George Boole (obrzek z Wikipedie)<| |  t33Logick opertory (funkce)VLogick sou in (a zroveH, AND) Y=A*B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vaechny vstupy=1 (stejn jako aritmetick sou in) Logick sou et (nebo, OR) Y=A+B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt alespoH jeden vstup=1 (1+1=1; nezamHujte s aritmetickm sou tem) )H)X )H  )XLogick opertory (funkce)Negace (inverze, NOT) Y= zmna 0-1 a naopak Vlu n nebo (exclusive OR, XOR) Y = A XOR B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vstupy rozn (prv jeden vstup je 1) odpovd spojce  , nebo s rkou bu, anebo  ale ne oba!/#$" "  "  "  "##$  $$("(: #  Logick opertory (funkce)NAND (Schefferova fce) negace sou inu (NOT AND) tabulka pro A,B,C,Y... ...Y=1, pokud alespoH 1 vstup nen 1 NOR (Piercova fce) negace sou tu (NOT OR) tabulka pro A,B,C,Y... ...Y=1, pokud ~dn vstup nen 1pUO<    "P \Q Logick opertory (funkce)&Dala: ekvivalence (rovnost) a=b y=a*b+anon*bnon antivalence (neekvivalence) inhibice (pYm, zptn) 1 ze 2 variant XORu implikace (pYm, zptn)5     n'  * Logick opertory (funkce)(napY. pYi programovn) mo~n pou~it na sla>1 (ne booleovsk) provd se samostatn po jednotlivch bitech napY. logick sou in x=5&6; //syntaxe C-like jazyko ... = 0101b & 0110b = 0100b = 4d napY. logick sou et 5|6= ? ... = 0101b | 0110b = 0111b = 7d => v pYpad logickch (nikoliv aritmetickch) opertoro tedy 5x6=4 5+6=7BZBZ@ZZ(Z>Z ZB"B")"*"*"*"*" " "*"*"*"*>" "v  *  ^ NGrafick zznam logickch fc/opertoro((( #AND (&), OR (1), NOT (o), NAND, NOR !Booleova algebra vizte pYednaku .5 komutativn, asociativn, distributivn a dala zkony&77"pln soubor logickch funkcrumo~Huje realizovat jakoukoliv logickou fci. (jakoukoliv kombinaci vstupo a vstupu) OR, AND, NOT pro n definovna Booleova algebra existuj dala pl. soubory l.f., ale nepou~vaj seLb#5 D#5>(I##Zpis logick fcebpravdivostn tabulka (vstupy, vstupy) algebraick vraz mapa (pYat) PY: napiate pravdivostn tabulky pro vrazy y=(a*b)+c y=(a+b)*c y=(*b)+c nakreslete zapojen (realizaci)\GlAl*"&  .HA &Z PYatDe Morganovy vztahy / zkony pYevod mezi sou inem a sou tem vysvtlen NOR a NAND realizovatelnost NOT, AND, OR jednm typem sou stky (nkolikerm pou~itm jedn fce) Karnaughovy mapy nzorn grafick 2D zobrazen, pYepis tabulky do algeb.vrazu nalezen podobnch kombinac, kter vedou ke stejnmu vsledku zjednoduaen logick funkce^ZZZZ  P  7c/l[g !"#  0 ,0(  ,x , c $p *0 `    x , c $ +0 `   H , 0޽h ? 3f{FEɄ___PPT10i.[g'+D=' I = @B +  # 0 ` \f(  \r \ S +B#style.visibility<*\Ht%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\t~%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\~%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(+r~R#s ZR10( / 0DArialngsRomanllyO 0DTimes New RomanllyO 0 DWingdingsRomanllyO 0@ . @n?" dd@  @@`` ` / /))*-+E\]hi/X$b$jsn 0AA @8  $Q ʚ;y8ʚ;g4jdjd O 0ppp@ <4dddd8v 0lpy <4!d!d8 0lg4SdSd O 08p@ pp<4BdBd8v 0lpy20___PPT10 pp___PPT9n3n)/ypf}I[ePNG  IHDR asRGB`PLTEkjjjUU@@@??@??+++**+**#g cmPPJCmp07128I tRNS@fAIDAT 0 ~{[8([Pz2S82(\dXP< zIENDB`0n&WvlHMU+vnPNG  IHDR asRGB`PLTEkjjkjjUUTU@@@??@++*+**M#A cmPPJCmp07128I tRNS@f>IDAT1W}{{J %s4!u61QJuRW&x&vxIENDB` ne!(mPɈPNG  IHDRysRGBPLTEffffffff̙̙O) cmPPJCmp0712 jtRNS ADIDATcP, SVA%6AC!P.iuD!".l`)SbPbL@]KIENDB`V#>?v, bPRIPO, cvi en  Ing. Martin Admek (UHK-FIM-KIT)O  =z .PRIPO Principy po ta o$P3.11.2009  cvi en . 7 Logick funkce $)'*Organiza n drobnosti dochzka F  $f:Binrn (booleovsk) promnn(<jedna slice dvojkov soustavy pravda x nepravda, true x false, 1 x 0 v praxi napY. 5V x 0V pYi programovn typ Bool(ean) George Boole (obrzek z Wikipedie)<| |  t33Logick opertory (funkce)VLogick sou in (a zroveH, AND) Y=A*B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vaechny vstupy=1 (stejn jako aritmetick sou in) Logick sou et (nebo, OR) Y=A+B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt alespoH jeden vstup=1 (1+1=1; nezamHujte s aritmetickm sou tem) )H)X )H  )XLogick opertory (funkce)Negace (inverze, NOT) Y= zmna 0-1 a naopak Vlu n nebo (exclusive OR, XOR) Y = A XOR B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vstupy rozn (prv jeden vstup je 1) odpovd spojce  , nebo s rkou bu, anebo  ale ne oba!/#$" "  "  "  "##$  $$("(: #  Logick opertory (funkce)NAND (Schefferova fce) negace sou inu (NOT AND) tabulka pro A,B,C,Y... ...Y=1, pokud alespoH 1 vstup nen 1 NOR (Piercova fce) negace sou tu (NOT OR) tabulka pro A,B,C,Y... ...Y=1, pokud ~dn vstup nen 1pUO<    "P \Q Logick opertory (funkce)&Dala: ekvivalence (rovnost) a=b y=a*b+anon*bnon antivalence (neekvivalence) inhibice (pYm, zptn) 1 ze 2 variant XORu implikace (pYm, zptn)5     n'  * Logick opertory (funkce)(napY. pYi programovn) mo~n pou~it na sla>1 (ne booleovsk) provd se samostatn po jednotlivch bitech napY. logick sou in x=5&6; //syntaxe C-like jazyko ... = 0101b & 0110b = 0100b = 4d napY. logick sou et 5|6= ? ... = 0101b | 0110b = 0111b = 7d => v pYpad logickch (nikoliv aritmetickch) opertoro tedy 5x6=4 5+6=7BZBZ@ZZ(Z>Z ZB"B")"*"*"*"*" " "*"*"*"*>" "v  *  ^ NGrafick zznam logickch fc/opertoro((( #AND (&), OR (1), NOT (o), NAND, NOR !Booleova algebra vizte pYednaku .5 komutativn, asociativn, distributivn a dala zkony&77"pln soubor logickch funkcrumo~Huje realizovat jakoukoliv logickou fci. (jakoukoliv kombinaci vstupo a vstupu) OR, AND, NOT pro n definovna Booleova algebra existuj dala pl. soubory l.f., ale nepou~vaj seLb#5 D#5>(I##Zpis logick fcebpravdivostn tabulka (vstupy, vstupy) algebraick vraz mapa (pYat) PY: napiate pravdivostn tabulky pro vrazy y=(a*b)+c y=(a+b)*c y=(*b)+c nakreslete zapojen (realizaci)\GlAl*"&  .HA &Z PYatDe Morganovy vztahy / zkony pYevod mezi sou inem a sou tem vysvtlen NOR a NAND realizovatelnost NOT, AND, OR jednm typem sou stky (nkolikerm pou~itm jedn fce) Karnaughovy mapy nzorn grafick 2D zobrazen, pYepis tabulky do algeb.vrazu nalezen podobnch kombinac, kter vedou ke stejnmu vsledku zjednoduaen logick funkce^ZZZZ  P  7c/l[g !"#rߑ#s o10( / 0DArialngsRomanllyO 0DTimes New RomanllyO 0 DWingdingsRomanllyO 0@ . @n?" dd@  @@`` ` / /))*-+E\]hi/X$b$jsn 0AA @8  $Q ʚ;y8ʚ;g4jdjd O 0ppp@ <4dddd8v 0lpy <4!d!d8 0lg4SdSd O 08p@ pp<4BdBd8v 0lpy20___PPT10 pp___PPT9n3n)/ypf}I[ePNG  IHDR asRGB`PLTEkjjjUU@@@??@??+++**+**#g cmPPJCmp07128I tRNS@fAIDAT 0 ~{[8([Pz2S82(\dXP< zIENDB`0n&WvlHMU+vnPNG  IHDR asRGB`PLTEkjjkjjUUTU@@@??@++*+**M#A cmPPJCmp07128I tRNS@f>IDAT1W}{{J %s4!u61QJuRW&x&vxIENDB` ne!(mPɈPNG  IHDRysRGBPLTEffffffff̙̙O) cmPPJCmp0712 jtRNS ADIDATcP, SVA%6AC!P.iuD!".l`)SbPbL@]KIENDB`V#>?v, bPRIPO, cvi en  Ing. Martin Admek (UHK-FIM-KIT)O  = .PRIPO Principy po ta o$P3.11.2009  cvi en . 7 Logick funkce $)'*Organiza n drobnosti dochzka F  $f:Binrn (booleovsk) promnn(<jedna slice dvojkov soustavy pravda x nepravda, true x false, 1 x 0 v praxi napY. 5V x 0V pYi programovn typ Bool(ean) George Boole (obrzek z Wikipedie)<| |  t33Logick opertory (funkce)VLogick sou in (a zroveH, AND) Y=A*B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vaechny vstupy=1 (stejn jako aritmetick sou in) Logick sou et (nebo, OR) Y=A+B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt alespoH jeden vstup=1 (1+1=1; nezamHujte s aritmetickm sou tem) )H)X )H  )XLogick opertory (funkce)Negace (inverze, NOT) Y= zmna 0-1 a naopak Vlu n nebo (exclusive OR, XOR) Y = A XOR B Pravdivostn tabulka: vizte tabuli pro vstup=1 mus bt vstupy rozn (prv jeden vstup je 1) odpovd spojce  , nebo s rkou bu, anebo  ale ne oba!/#$" "  "  "  "##$  $$("(: #  Logick opertory (funkce)NAND (Schefferova fce) negace sou inu (NOT AND) tabulka pro A,B,Y... ...Y=1, pokud alespoH 1 vstup nen 1 NOR (Piercova fce) negace sou tu (NOT OR) tabulka pro A,B,Y... ...Y=1, pokud ~dn vstup nen 1pSM:    "b Z%% Logick opertory (funkce)&Dala: ekvivalence (rovnost) a=b y=a*b+anon*bnon antivalence (neekvivalence) inhibice (pYm, zptn) 1 ze 2 variant XORu implikace (pYm, zptn)5     n'  * Logick opertory (funkce)(napY. pYi programovn) mo~n pou~it na sla>1 (ne booleovsk) provd se samostatn po jednotlivch bitech napY. logick sou in x=5&6; //syntaxe C-like jazyko ... = 0101b & 0110b = 0100b = 4d napY. logick sou et 5|6= ? ... = 0101b | 0110b = 0111b = 7d => v pYpad logickch (nikoliv aritmetickch) opertoro tedy 5x6=4 5+6=7BZBZ@ZZ(Z>Z ZB"B")"*"*"*"*" " "*"*"*"*>" "v  *  ^ NGrafick zznam logickch fc/opertoro((( #AND (&), OR (1), NOT (o), NAND, NOR !Booleova algebra vizte pYednaku .5 komutativn, asociativn, distributivn a dala zkony&77"pln soubor logickch funkcrumo~Huje realizovat jakoukoliv logickou fci. (jakoukoliv kombinaci vstupo a vstupu) OR, AND, NOT pro n definovna Booleova algebra existuj dala pl. soubory l.f., ale nepou~vaj seLb#5 D#5>(I##Zpis logick fcebpravdivostn tabulka (vstupy, vstupy) algebraick vraz mapa (pYat) PY: napiate pravdivostn tabulky pro vrazy y=(a*b)+c y=(a+b)*c y=(*b)+c nakreslete zapojen (realizaci)\GlAl*"&  .HA &Z PYatDe Morganovy vztahy / zkony pYevod mezi sou inem a sou tem vysvtlen NOR a NAND realizovatelnost NOT, AND, OR jednm typem sou stky (nkolikerm pou~itm jedn fce) Karnaughovy mapy nzorn grafick 2D zobrazen, pYepis tabulky do algeb.vrazu nalezen podobnch kombinac, kter vedou ke stejnmu vsledku zjednoduaen logick funkce^ZZZZ  P  7c/l[g !"#  0 ,0(  ,x , c $p *0 `    x , c $ +0 `   H , 0޽h ? 3f{FEɄ___PPT10i.[g'+D=' I = @B +r=s 1