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AXIOMA pada aljabar BooleA1: Idempotent : a.a = a ; a + a = a
A2: Commutative: a.b = b.a ; a + b = b + a
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 = a
a.0 = 0.a = 0 ; a + 1 = 1 + a = 1
A7: Complement : a.ā = 0 ; a + ā = 1
A1: Idempotent : a.a = a ; a + a = a
A2: Commutative: a.b = b.a ; a + b = b + a
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 = a
a.0 = 0.a = 0 ; a + 1 = 1 + a = 1
A7: Complement : a.ā = 0 ; a + ā = 1
MINIMISASI SUATU
RANGKAIAN DIGITAL
denganPETA KARNAUGH (PK)
(KARNAUGH MAP)
MINIMISASI SUATU
RANGKAIAN DIGITAL
denganPETA KARNAUGH (PK)
(KARNAUGH MAP)
AB
0 1
PETA KARNAUGH 2 VARIABEL
AB
SISTEM DIGITAL- GPO 3
Nomor urut decimalkotak data PK 2 variabel
AB
0 1
0 AB (00)
0AB (10)
2
1AB (01)
1AB (11)
3
Y = A Y = A Y = B Y = BA
B 0 1A
B 0 1A
B 0 1A
B 0 1
0 1 0 1 0 0 1 11 1 1 1 1 1 1 1
Y = A B Y = AB Y = AB Y = ABA
B 0 1A
B 0 1A
B 0 1A
B 0 1
0 1 0 0 1 0
1 1 1 1 1 1
Buat persamaan boolean dari PK berikut0 1 0 1 0 1
0 1 0 1 0 1 11 1 1 1 1 1 1 1
0 1 0 1 0 1
Y =
Y = Y = Y =
Y = Y =
SISTEM DIGITAL- GPO 5
0 1 0 1 0 1
0 1 1 0 1 0 11 1 1 1 1 1
0 1 0 1 0 1
0 0 0 11 1 1 1 1
Y = Y = Y =
Sederhanakan rangkaian berikutdengan PK
SISTEM DIGITAL- GPO 6
Nomor urut decimalkotak data PK
3 variabelABC
ABC 00 01 11 10
ABC(000)
0
ABC(010)
2
ABC(110)
6
ABC(100)
4
PETA KARNAUGH 3 VARIABELABC
SISTEM DIGITAL- GPO
Nomor urut decimalkotak data PK
3 variabelABC
0ABC
(000)
0
ABC(010)
2
ABC(110)
6
ABC(100)
4
1ABC(001)
1
ABC(011)
3
ABC(111)
7
ABC(101)
5
Tata letak variabel00 01 11 10 00 01 11 10
0 1 1 0 1 11 1 1 1 1 1
Y = Y =00 01 11 10 00 01 11 10
0 1 1 0 1 1
SISTEM DIGITAL- GPO 8
0 1 1 0 1 11 1 1 1 1 1
Y = Y =00 01 11 10 00 01 11 10
0 0 1 1 1 11 1 1 1 1 1
Y = Y =
Buat persamaan boolean dari PK berikut:00 01 11 10 00 01 11 10
0 1 1 0 1 1 1 11 1 1 1 1 1 1 1
Y = Y =00 01 11 10 00 01 11 10
0 1 1 1 1 0 1 1
SISTEM DIGITAL- GPO 9
0 1 1 1 1 0 1 11 1 1 1 1 1 1 1
Y = Y =00 01 11 10 00 01 11 10
0 1 1 1 0 1 1 1 11 1 1 1 1
Y =Y =
Buat persamaan boolean dari PK berikut:00 01 11 10 00 01 11 10
0 1 0 1 1 11 1 1 1 1 1
Y = Y =00 01 11 10 00 01 11 10
0 1 1 1 0 1 1
SISTEM DIGITAL- GPO 10
0 1 1 1 0 1 11 1 1 1 1
Y = Y =00 01 11 10 00 01 11 10
0 1 1 0 1 1 11 1 1 1 1
Y =Y =
Buat persamaan boolean dari PK berikut:Y= Y=00 01 11 10 00 01 11 10
0 1 0 1 1 11 1 1 1 1 1 1 1 1
Y = Y =00 01 11 10 00 01 11 10
SISTEM DIGITAL- GPO 11
00 01 11 10 00 01 11 10
0 1 1 0 1 11 1 1 1 1 1 1
Y = Y =00 01 11 10 00 01 11 10
0 1 1 0 1 1 11 1 1 1 1
