ؿf(A1,A2,A3,,An)ȤȤѿAiΤȤ͡ˤ0ޤ1Ǥ롣äơؿȤοˤäơ¸ߤؿꤹ롣
㤨Сn=1ΤȤϡϤҤȤĤʤΤؿf(A)ηɽ롣f(A)Ϥ012̤Ǥ롣줾AͤȤ߹碌Фơf(A)ͰȤ0ޤ1Ȥ롣ȤȤϡA2̤ꡢf(A)2̤4ĤΥѥ¨4Ĥδؿfͤ뤳ȤǤ롣
A | f0 | f1 | f2 | f3 |
0 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 1 |
ؿf0ϡϤƤ0Ϥ롣
ؿf1ϡf1=AǤ롣
ؿf2ϡf2=AǤ롣
ؿf3ϡϤƤ1Ϥ롣
Ʊͤ2ѿξΤȤؿͤ뤳ȤǤ롣ξϡf(A,B)ȤʤꡢAB줾0ޤ1ȤʤꡢȤ߹碌4̤ꤢ롣4̤Ȥ߹碌줾ˤĤơ0ޤ1νϤͤ롣äơؿ16ˤʤ롣
A | B | f0 | f1 | f2 | f3 | f4 | f5 | f6 | f7 | f8 | f9 | f10 | f11 | f12 | f13 | f14 | f15 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
16ؿfABǹɽǤ롣ˤĤפʴؿƤ
ؿ | ̾ | |
f0 | ̿ʹ | 0 |
f1 | ѡAND | AB |
f3 | A | A |
f5 | B | B |
f6 | ¾Ū¡XOR | ABAB |
f7 | ¡OR | AB |
f8 | ¤ | AB |
f13 | AB | |
f14 | Ѥ | AB |
f15 | ̿ʹ | 1 |
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
ޤ٤2ĤΰΤȤƤ
ɽf14(A,B)ΤȤȴФƤ
A | B | f14 |
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
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
ѿnĤϤδؿˤĤƼΩġ
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
ˡɸϤħȤƼ롣
äơΥŸ줿ؿ˿ͤΤǤϤʤɽ1θĽܤؿ櫓
Τ褦f(A,B)οɽäȤ롣
A | B | f(A,B) |
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 0 |
1 | 1 | 1 |
ɽf(A,B)ؿΤꤿȤ롣ΥŸȤäƵƤ褤櫓ѷǤäȥƥ˥ɬפǤʷ̤ϡABˡ
ǡΤ褦ɽ롣ñ3ܤ4ܤΰ֤Ǥ롣
A | B | f(A,B) |
0 | 0 | 1 |
0 | 1 | 1 |
1 | 1 | 1 |
1 | 0 | 0 |
[ͻ1]ʤΤ褦ΤȤȡϥߥΥ1ˤʤäƤõ䤹뤿Ǥ롣
[ͻ2]1ܤ2ܡ2ܤ3ܡ3ܤ4ܡ4ܤ1ܤϤ줾ϥߥΥ1ˤʤäƤ롣
Τ褦ˤơѷǤʹबܤ褦˹Ԥ¤١οɽǤΰִطǹƳФǤ뤫ɤȽǤǤ褦ˤʤ롣Τ褦¤٤ɽΡȤ
̤˥ΡޤϼΤ褦˽IJοޤɽ롣ۤɤɽȼΤ褦ˤʤ롣
ԤAB | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1ΤȤ˴ݰĤƤߤޤ礦4ĤʬΤ3ġʡABABABˤ1ˤʤäƤ뤬3ĤιफϤƤޤȼѷʤäƤޤ
Ρޤ褯ߤȡܤƱΤǼΤ褦ѷǤ뤳Ȥ狼Ϥ
2ĤѷʬʱߤǤäƤߤ롣ȡɽˤؿϡ2Ĥʱߤζʬˤʤ롣äơABȴñˤ狼롣
ޤǽ褯ɤǤϥΥŸǡˤϤΥΡޤǤФ䤯ǤѤȤդ櫓ǰŪʤ顢ΥΡޤβλǤлȤǤϽʬʤȤʤ
㤨СǤΡ33ޤǤΡ˹ηΤȤ˥饹ˡǷƤޤƱͤäǤ롣
[]
ABCD | 00 | 01 | 11 | 10 |
00 | 1 | 0 | 0 | 1 |
01 | 0 | 1 | 1 | 0 |
11 | 0 | 1 | 1 | 0 |
10 | 0 | 0 | 0 | 0 |
äơ
Ρޤؿˡϡ4ѿ٤Ǥдñ˹Ԥ롣ºݤˤƴΤ֤
7LED10ʿ1ɽϩǤ롣ABCD4ӥåȡag7ĤLEDǤ롣㤨ABCD=0000ϤС0ɽa,b,c,d,e,fLEDˡޤABCD=0101Ϥ5ɽa,c,d,f,gLEDˡ
[]dʰդLEDˤɽ뤿ؿͤ롣
dʬΤϡ7LED0,2,3,5,6,86ĤξǤ롣
dؿμˡɸϼΤ褦ˤʤ롣
ˡؿΡޤѤƴά롣
14ѿΡޤd6ĤκǾΤȤ1Ƚࡣ
2ȸΩ1ϡκǾǤ롣
34Ȥ1ˤϴޤޤʤ2Ȥ1ʬʱߤǽȾʱߤϸ¦ȷҤˡ,
,
,
4Ĥ롣
4ʾ4ȰʾϤʤ٤Ƥ1ʱߤǰϤޤ줿ϼ5ĤȤʤ롣
5ΤʳɬܹȤʤʥåդƤˡơɬܹϼ4ĤȤʤ롣
6椨˴ά줿ؿϼ̤Ǥ롣
ŻҲϩˤDon't CareȤǰ롣㤨3ĤΥåIJ餫ΥǥϩäȤơΥå3ƱONˤ뤳Ȥʤ硢νϤˤĤƹͤɬפʤĤޤꡢ3ƱONˤ褦ʤȤνϤ0Ǥ1Ǥʤ櫓Ǥ롣Τ褦ʽϤDon't careʶػߡĹȸƤ֡Don't Careϡɽǡ֦աפȤƵҤ롣
ΡޤʱߤǰϤȤˡDon't CareʬϰϤǤ褤ϤޤʤƤ褤櫓ΡޤʱߤȤμͳ٤ޤ櫓ǡΨΤ褤ʱߤȤǤ롣
Don't Careޤɽΰ롣
A | B | C | f(A,B,C) |
0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | |
1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 |
1 | 1 | 1 |
ΡޤѴȼΤ褦ˤʤ롣
äơؿϡf(A,B,C)ABCȤʤ롣
ΡޤϳΤǽǤϤʤΡޤǴñؿ뤳ȤǤΤ4ѿޤǤǡפƤ5ѿ³Ǥ롣ºݤˤϤʾѿäƤƤ⸶Ū˥Ρޤǹͤ뤳ȤǤ뤬ʱߤǰϤȤθȤְ㤤¿ʤäƤޤΤǤ롣ǤϥΡޤФ̣ʤ
ǡ5ѿʾؿκȤƿˡͤɬפ롣
Ρޤܤ1иĽʱߤǰϤǤϡδά㤨СAˡA1ʤɡˤ櫓
ȡܤĽΨ褯ϳʤĤ뤳ȤǤСΡޤȤʤƤ褤櫓
Quine-MeCluskeyʥ磻ޥ饹ˡȤϡϥߥΥѤؿˡǤ롣
ϥߥΥϼDHǵ͡ʵΥˤǤ롣
ޤɽؿ
A | B | C | f(A,B,C) |
0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 1 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 0 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 |
ޤϥߥΥνˡͤ1ȤʤäƤ夫¤٤롣¤ӽȼΤ褦ˤʤ롣
ʤ狼䤹褦ˤ줾ι˭ֹդƤ롣
ˡѿҤȤĸ餷Τ¦ɲä롣ΤȤϥߥΥ1Ǥ2Ĥιõơ¤롣
ƱͤˤơѿҤȤĤˤʤޤǷ֤
ǡΤ٤Ƥޤ褦ȹ碌ͤ롣ĤΥѥͤ뤬Ȥ߹碌ĿäȤ⾯ʤȹ碌褦ˤ롣
ȭBȤ߹碌뤳Ȥǡ٤ƴޤࡣäơؿ
뤳ȤǤ롣