LOGINFO 0597
AXIOMA
pada aljabar Boole
A1: Idempotent : a.a = a
; a+a=a
A2: Commutative: a.b = b.a
a
; a+b=b+
A3: Associative : a.(b.c) = (a.b).c; a + (b+c) =
(a+b) + c
A4: Absorbtive :a.(a + b) = a
; a + (a.b) = a
A5: Distributive : a.(b + c) = (a.b) + (a.c) ;
a + (b.c) = (a + b).(a
+ c)
A6: Elemen Unik : a.1 = 1.a = a
;a+0=0+a
MINIMISASI SUATU
RANGKAIAN DIGITAL
dengan
PETA KARNAUGH (PK)
(KARNAUGH MAP)
PETA KARNAUGH 2 VARIABEL
AB
A
B
Nomor urut decimal
kotak data PK 2 variabel
AB
0
1
SISTEM DIGITAL- GPO
0
1
AB (00)
AB
(10)
0
2
AB (01)
AB
(11)
1
3
3
Y=A
Y=A
A
0
B
1
A
B
Y=B
A
0
1
1
0
1
0
1
1
1
1
1
Y = AB
A
0
B
0
1
1
1
A
B
1
B
0
1
1
0
1
Y = AB
0
1
1
1
1
1
Y = AB
A
0
B
0
1
A
0
1
A
0
B
0
Y=AB
Y=B
1
1
0
B
1
0
1
1
Buat persamaan boolean dari PK
berikut
Y=
Y=
Y=
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
Y=
0
0
1
0
1
1
1
1
Y=
1
1
1
Y=
1
0
1
1
0
Y=
Y=
0
1
0
1
0
1
Y=
1
0
0
1
SISTEM DIGITAL- GPO
1
1
1
0
1
0
1
1
1
5
Sederhanakan rangkaian berikut
dengan PK
SISTEM DIGITAL- GPO
6
PETA KARNAUGH 3 VARIABEL
ABC
AB
C
Nomor urut decimal
kotak data PK
3 variabel
ABC
0
1
00
01
11
10
ABC
(000)
ABC
(010)
ABC
(110)
ABC
(100)
0
2
6
4
ABC
(001)
ABC
(011)
ABC
(111)
ABC
(101)
1
3
7
5
SISTEM DIGITAL- GPO
Tata letak
00 01 11 10
1 1
0
1 1
1
variabel
00 01 11 10
0 1 1
1 1 1
Y=
Y=
00 01 11 10
1 1
0
1 1
1
00 01 11 10
1
0 1
1
1 1
Y=
Y=
00 01 11 10
00 01 11 10
0 1 1 1 1
1 1
Y=
1
0
1
1
1
SISTEM DIGITAL- GPO
Y=
8
Buat persamaan boolean dari PK
berikut:
00 01 11 10
1 1
0
1 1 1 1 1
00 01 11 10
0 1 1 1 1
1
1 1
Y=
Y=
00 01 11 10
0 1 1 1 1
1 1
1
00 01 11 10
1
0 1
1 1 1 1 1
Y=
Y=
00 01 11 10
1 1 1
0
1 1
1
Y=
00 01 11 10
0 1 1 1 1
1
1
Y=
SISTEM DIGITAL- GPO
9
Buat persamaan boolean dari PK
berikut:
00 01 11 10
1
0
1
1 1 1
00 01 11 10
1 1 1
0
1 1
Y=
Y=
00 01 11 10
1 1
0 1
1
1
00 01 11 10
1
1
0
1
1 1
Y=
Y=
00 01 11 10
1 1
0
1 1
1
Y=
00 01 11 10
0 1 1 1
1
1
Y=
SISTEM DIGITAL- GPO
10
Buat persamaan boolean dari PK
berikut: Y
Y
=
00
=
01
11
0
1
1
1
1
10
00
1
0
1
1
1
1
Y=
00
0
01
11
10
1
1
1
00
0
1
10
1
1
1
1
01
11
10
0
1
1
1
1
1
1
01
11
10
1
1
1
Y=
00
11
Y=
1
1
01
Y=
01
11
1
1
10
00
1
0
1
1
SISTEM DIGITAL- GPO
1
11
pada aljabar Boole
A1: Idempotent : a.a = a
; a+a=a
A2: Commutative: a.b = b.a
a
; a+b=b+
A3: Associative : a.(b.c) = (a.b).c; a + (b+c) =
(a+b) + c
A4: Absorbtive :a.(a + b) = a
; a + (a.b) = a
A5: Distributive : a.(b + c) = (a.b) + (a.c) ;
a + (b.c) = (a + b).(a
+ c)
A6: Elemen Unik : a.1 = 1.a = a
;a+0=0+a
MINIMISASI SUATU
RANGKAIAN DIGITAL
dengan
PETA KARNAUGH (PK)
(KARNAUGH MAP)
PETA KARNAUGH 2 VARIABEL
AB
A
B
Nomor urut decimal
kotak data PK 2 variabel
AB
0
1
SISTEM DIGITAL- GPO
0
1
AB (00)
AB
(10)
0
2
AB (01)
AB
(11)
1
3
3
Y=A
Y=A
A
0
B
1
A
B
Y=B
A
0
1
1
0
1
0
1
1
1
1
1
Y = AB
A
0
B
0
1
1
1
A
B
1
B
0
1
1
0
1
Y = AB
0
1
1
1
1
1
Y = AB
A
0
B
0
1
A
0
1
A
0
B
0
Y=AB
Y=B
1
1
0
B
1
0
1
1
Buat persamaan boolean dari PK
berikut
Y=
Y=
Y=
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
Y=
0
0
1
0
1
1
1
1
Y=
1
1
1
Y=
1
0
1
1
0
Y=
Y=
0
1
0
1
0
1
Y=
1
0
0
1
SISTEM DIGITAL- GPO
1
1
1
0
1
0
1
1
1
5
Sederhanakan rangkaian berikut
dengan PK
SISTEM DIGITAL- GPO
6
PETA KARNAUGH 3 VARIABEL
ABC
AB
C
Nomor urut decimal
kotak data PK
3 variabel
ABC
0
1
00
01
11
10
ABC
(000)
ABC
(010)
ABC
(110)
ABC
(100)
0
2
6
4
ABC
(001)
ABC
(011)
ABC
(111)
ABC
(101)
1
3
7
5
SISTEM DIGITAL- GPO
Tata letak
00 01 11 10
1 1
0
1 1
1
variabel
00 01 11 10
0 1 1
1 1 1
Y=
Y=
00 01 11 10
1 1
0
1 1
1
00 01 11 10
1
0 1
1
1 1
Y=
Y=
00 01 11 10
00 01 11 10
0 1 1 1 1
1 1
Y=
1
0
1
1
1
SISTEM DIGITAL- GPO
Y=
8
Buat persamaan boolean dari PK
berikut:
00 01 11 10
1 1
0
1 1 1 1 1
00 01 11 10
0 1 1 1 1
1
1 1
Y=
Y=
00 01 11 10
0 1 1 1 1
1 1
1
00 01 11 10
1
0 1
1 1 1 1 1
Y=
Y=
00 01 11 10
1 1 1
0
1 1
1
Y=
00 01 11 10
0 1 1 1 1
1
1
Y=
SISTEM DIGITAL- GPO
9
Buat persamaan boolean dari PK
berikut:
00 01 11 10
1
0
1
1 1 1
00 01 11 10
1 1 1
0
1 1
Y=
Y=
00 01 11 10
1 1
0 1
1
1
00 01 11 10
1
1
0
1
1 1
Y=
Y=
00 01 11 10
1 1
0
1 1
1
Y=
00 01 11 10
0 1 1 1
1
1
Y=
SISTEM DIGITAL- GPO
10
Buat persamaan boolean dari PK
berikut: Y
Y
=
00
=
01
11
0
1
1
1
1
10
00
1
0
1
1
1
1
Y=
00
0
01
11
10
1
1
1
00
0
1
10
1
1
1
1
01
11
10
0
1
1
1
1
1
1
01
11
10
1
1
1
Y=
00
11
Y=
1
1
01
Y=
01
11
1
1
10
00
1
0
1
1
SISTEM DIGITAL- GPO
1
11