ΥڡϤƤʥ֥åޡɲΥڡޤϤƤʥ֥åޡ Υڡlivedoor åפɲΥڡޤlivedoor å

ܼ

ؿ

ؿf(A1,A2,A3,,An)ȤȤѿAiΤȤ͡ˤ0ޤ1Ǥ롣äơؿȤοˤäơ¸ߤؿꤹ롣

㤨Сn=1ΤȤϡϤҤȤĤʤΤؿf(A)ηɽ롣f(A)Ϥ012̤Ǥ롣줾AͤȤ߹碌Фơf(A)ͰȤ0ޤ1Ȥ롣ȤȤϡA2̤ꡢf(A)2̤4ĤΥѥ¨4Ĥδؿfͤ뤳ȤǤ롣

Af0f1f2f3
00011
10101

ؿf0ϡϤƤ0Ϥ롣
ؿf1ϡf1=AǤ롣
ؿf2ϡf2=AǤ롣
ؿf3ϡϤƤ1Ϥ롣

Ʊͤ2ѿξΤȤؿͤ뤳ȤǤ롣ξϡf(A,B)ȤʤꡢAB줾0ޤ1ȤʤꡢȤ߹碌4̤ꤢ롣4̤Ȥ߹碌줾ˤĤơ0ޤ1νϤͤ롣äơؿ16ˤʤ롣

ABf0f1f2f3f4f5f6f7f8f9f10f11f12f13f14f15
000000000011111111
010000111100001111
100011001100110011
110101010101010101

16ؿfABǹɽǤ롣ˤĤפʴؿ򼨤Ƥ

ؿ̾
f0̿ʹ0
f1ѡANDAB
f3AA
f5BB
f6¾Ū¡XORABAB
f7¡ORAB
f8¤AB
f13AB
f14ѤAB
f15̿ʹ1

ΥŸ

n=1¨ҤȤĤȤȤɽƤӸƤ餤褯ȵդ⤷ʤΩġ

f(A)=f(0)f2f(1)3 f(A)=f(0)Af(1)A

μ0ȼΤ褦˷׻Ǥ롣

f(0) =f(0)0f(1)0 =f(0)1 =f(0)

μ1ȼΤ褦˷׻Ǥ롣

f(1) =f(0)1f(1)1 =f(0)0f(1)1 =f(1)

äơؿf(A)=f(0)Af(1)AAͤ0,1ɤǤäƤ⤽줾οͤ롣

椨ˡ֢Af(A)=f(0)Af(1)AפΩĤȤȤˤʤ롣

ޤ٤2ĤΰΤȤ򸫤Ƥ

ɽf14(A,B)ΤȤȴФƤ

ABf14
001
011
101
110

줫鼡Ωġ

f14(A,B)
=f(0,0)ABf(0,1)ABf(1,0)ABf(1,1)AB
=1AB1AB1AB0ABʢɽ
=ABˡABAB
=ABˡABˡABABʢ衱AB˱黻ɲä̤ϤʤOK
=ABˡABˡABABʢ¤ؤ
=A(BBˢˡBʡAA
=AˡBʢȡȥ
=(AB

[]ΥŸ
ѿnĤ΢ϤδؿˤĤƼΩġ
f(A1,A2,A3,,An)=f(0,A2,A3,,An)A1f(1,A2,A3,,An)A1

nĤΰf(A1,A2,A3,,An)n-1ĤΤf(0,A2,A3,,An)A1f(1,A2,A3,,An)A1ȤؿѴƤ롣

ĤޤꡢؿΰҤȤĸ餷Ƥ櫓Τ褦ˤơοҤȤĤĸ餷ƤȡǽŪˤؿͤɽǤ롣Τ褦ˤƺǽŪɽΤˡɸȤ

ˡɸϤħȤƼ󤲤롣

  • ɽ1ȤʤäƤĽбबޤޤ롣
  • 줾ιϡФƹ1ˤ褦ˤʤäƤ롣

äơΥŸ줿ؿ˿ͤΤǤϤʤɽ1θĽܤؿ櫓

Ρ

Τ褦f(A,B)οɽäȤ롣

ABf(A,B)
001
011
100
111

ɽf(A,B)ؿΤꤿȤ롣ΥŸȤäƵƤ褤櫓ѷǤäȥƥ˥ɬפǤʷ׻̤ϡABˡ

ǡΤ褦ɽ񤭴롣ñ3ܤ4ܤΰ֤򴹤Ǥ롣

ABf(A,B)
001
011
111
100

[ͻ1]ʤΤ褦򤷤ΤȤȡϥߥ󥰵Υ1ˤʤäƤõ䤹뤿Ǥ롣

[ͻ2]1ܤ2ܡ2ܤ3ܡ3ܤ4ܡ4ܤ1ܤϤ줾ϥߥ󥰵Υ1ˤʤäƤ롣

Τ褦ˤơѷǤʹबܤ褦˹Ԥ¤١οɽǤΰִط򸫤ǹƳФǤ뤫ɤȽǤǤ褦ˤʤ롣Τ褦¤٤ɽΡȤ

̤˥ΡޤϼΤ褦˽IJοޤɽ롣ۤɤɽ񤭴ȼΤ褦ˤʤ롣

ԤAB01
011
101

1ΤȤ˴ݰĤƤߤޤ礦4ĤʬΤ3ġʡABABABˤ1ˤʤäƤ뤬3Ĥιफ׻ϤƤޤȼѷ񤷤ʤäƤޤ

Ρޤ褯ߤȡܤƱΤǼΤ褦ѷǤ뤳Ȥ狼Ϥ

  • ABˡABᡱA
  • ABABB

2ĤѷʬʱߤǤäƤߤ롣ȡɽˤؿϡ2Ĥʱߤζʬˤʤ롣äơABȴñˤ狼롣

ޤǽ褯ɤǤϥΥŸ򤭤򤷤ǡ׻ˤϤΥΡޤǤФ䤯׻ǤѤȤդ櫓ǰ׻Ūʤ顢ΥΡޤβλǤлȤǤϽʬʤȤʤ

㤨СǤΡ33ޤǤΡ˹󼰤η׻ΤȤ˥饹ˡǷ׻ƤޤƱͤäǤ롣

[]

ABCD00011110
001001
010110
110110
100000
  • ԥ󥯿ʬꡢ\bar{A}\cdot\bar{B}\cdot\bar{D}
  • ĿʬꡢB~\cdot~D

äơ\bar{A}\cdot\bar{B}\cdot\bar{D}~+~B~\cdot~D

ʣʥΡ

Ρޤؿˡϡ4ѿ٤Ǥдñ˹Ԥ롣ºݤˤ򤤤ƴΤ֤

7LEDؿ

7LED10ʿ1ɽϩǤ롣ABCD4ӥåȡag7ĤLEDǤ롣㤨ABCD=0000ϤС0ɽa,b,c,d,e,fLEDˡޤABCD=0101Ϥ5ɽa,c,d,f,gLEDˡ

[]dʰդLEDˤɽ뤿ؿͤ롣

dʬΤϡ7LED0,2,3,5,6,86ĤξǤ롣

  • ABCD=00000
  • ABCD=00102
  • ABCD=00113
  • ABCD=01015
  • ABCD=01106
  • ABCD=10008

dؿμˡɸϼΤ褦ˤʤ롣

d~=~\bar{A}\bar{B}\bar{C}\bar{D}~+~\bar{A}\bar{B}C\bar{D}~+~\bar{A}\bar{B}CD~+~\bar{A}B\bar{C}D~+~\bar{A}BC\bar{D}~+~A\bar{B}\bar{C}\bar{D}

ˡؿ򥫥ΡޤѤƴά롣

14ѿΡޤd6ĤκǾΤȤ1Ƚ񤭹ࡣ

2ȸΩ1ϡ\bar{A}B\bar{C}DκǾǤ롣

34Ȥ1ˤϴޤޤʤ2Ȥ1ʬʱߤǽ񤭹Ⱦʱߤϸ¦ȷҤˡ\bar{B}\bar{C}\bar{D},\bar{A}\bar{B}\bar{D},\bar{A}\bar{B}C,\bar{A}C\bar{D}4Ĥ롣

4ʾ4ȰʾϤʤ٤Ƥ1ʱߤǰϤޤ줿ϼ5ĤȤʤ롣

  • \bar{A}B\bar{C}D
  • \bar{B}\bar{C}\bar{D}
  • \bar{A}\bar{B}\bar{D}
  • \bar{A}\bar{B}C
  • \bar{A}C\bar{D}

\bar{A}\bar{B}\bar{D}ʳɬܹȤʤʥåդƤˡơɬܹϼ4ĤȤʤ롣

  • \bar{A}B\bar{C}D
  • \bar{B}\bar{C}\bar{D}
  • \bar{A}\bar{B}C
  • \bar{A}C\bar{D}

6椨˴ά줿ؿϼ̤Ǥ롣

d~=~\bar{A}B\bar{C}D~+~\bar{B}\bar{C}\bar{D}~+~\bar{A}\bar{B}C~+~\bar{A}C\bar{D}

Don't Care

ŻҲϩˤDon't CareȤǰ롣㤨3ĤΥåIJ餫ΥǥϩäȤơΥå3ƱONˤ뤳Ȥʤ硢νϤˤĤƹͤɬפʤĤޤꡢ3ƱONˤ褦ʤȤνϤ0Ǥ1Ǥ⹽ʤ櫓Ǥ롣Τ褦ʽϤDon't careʶػߡĹȸƤ֡Don't Careϡɽǡ֦աפȤƵҤ롣

ΡޤʱߤǰϤȤˡDon't CareʬϰϤǤ褤ϤޤʤƤ褤櫓ΡޤʱߤȤμͳ٤ޤ櫓ǡΨΤ褤ʱߤȤǤ롣

Don't Careޤ࿿ɽΰ󤲤롣

ABCf(A,B,C)
0000
0011
0100
011
1000
1011
1101
111

򥫥ΡޤѴȼΤ褦ˤʤ롣

karuno1.jpg

äơؿϡf(A,B,C)ABCȤʤ롣

ؿδάΥץ

  • ؿѷˤά
    • ؿ˴ؤѤѷñʲϩƳˡ
  • Veitchޤ䥫Ρޤʤɤˤά
    • ؿ޼޷Ū˴άԤˡ
    • Ū˹ԤΤǽ鿴Ը
    • ϤοˤĤƿޤ礭ʣˤʤΤǡ5İʾϤIJϩˤԸǤ롣
  • 磻-ޥ饹Quine-McClukeyˡˤά
    • ԥ塼ѤơưŪ˴άԤΤŬˡ
    • ¿ϤIJϩǤάǽǤ롣

Quine-MeCluskeyˡ

ΡޤϳΤǽǤϤʤΡޤǴñؿ뤳ȤǤΤ4ѿޤǤǡפƤ5ѿ³Ǥ롣ºݤˤϤʾѿäƤƤ⸶Ū˥Ρޤǹͤ뤳ȤǤ뤬ʱߤǰϤȤθȤְ㤤¿ʤäƤޤΤǤ롣ǤϥΡޤФ̣ʤ

ǡ5ѿʾؿκȤƿˡͤɬפ롣

Ρޤܤ1иĽʱߤǰϤǤϡδά㤨СAˡA1ʤɡˤ櫓

ȡܤĽΨ褯ϳʤĤ뤳ȤǤСΡޤȤʤƤ褤櫓

Quine-MeCluskeyʥ磻󡦥ޥ饹ˡȤϡϥߥ󥰵ΥѤؿˡǤ롣

ϥߥ󥰵ΥϼDHǵ͡ʵΥˤǤ롣

\normalsize\displaystyle~D_H=\normalsize~{\sum_{i=1}^na_i~\oplus~b_i}

ޤɽؿ򼨤

ABCf(A,B,C)
0001
0010
0101
0111
1000
1010
1101
1111

ޤ\widebar{A}~\widebar{B}~\widebar{C}ϥߥ󥰵Υνˡͤ1ȤʤäƤ夫¤٤롣¤ӽȼΤ褦ˤʤ롣

ʤ狼䤹褦ˤ줾ι˭ֹդƤ롣

ˡѿҤȤĸ餷Τ¦ɲä롣ΤȤϥߥ󥰵Υ1Ǥ2Ĥιõơ¤롣

ƱͤˤơѿҤȤĤˤʤޤǷ֤

ǡΤ٤Ƥޤ褦ȹ碌ͤ롣ĤΥѥ󤬹ͤ뤬Ȥ߹碌ĿäȤ⾯ʤȹ碌򤹤褦ˤ롣 \widebar{A}~\widebar{C}ȭBȤ߹碌뤳Ȥǡ򤹤٤ƴޤࡣäơؿ\widebar{A}~\widebar{C}~\wedge~B뤳ȤǤ롣

ʸ

  • عʷϤ١ʥåȥƥ
  • إ饹ȡ޲򡡥ǥϩΤߤ狼ܡ
  • ؾѼԻݥåȥǥѾ󵻽Ѽԡ
  • إԥ塼ưߡ

źեե: filekaruno1.jpg 3115 [ܺ]