agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-karnaugh-map.pdfagenda chapter 1 –k-map 2...
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![Page 1: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/1.jpg)
Agenda
Chapter 1 – K-Map 2 Variabel
1. Model K-Map 2 Variabel
2. Desain Pemetaan K-Map 2 Variabel
Chapter 2 – K-Map 3 Variabel
Chapter 3 – K-Map 4 Variabel
Chapter 4 – Don’t Care
![Page 2: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/2.jpg)
Peta Karnaugh / Karnaugh Map
• Suatu peralatan grafis yang digunakan untuk menyederhanakan persamaan
logika atau mengkonversikan sebuah tabel kebenaran menjadi sebuah
rangkaian logika
m0 m2
m1 m3
0 1
0
1
A
BA B f(A,B)
0 0 0
0 1 0
1 0 0
1 1 1
![Page 3: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/3.jpg)
K Map-2 Variabel
Map
ValuesA B Y
0 0 0 A’B’
1 0 1 A’B
2 1 0 AB’
3 1 1 AB
Tabel Kebenaran
MODE 1
A’B’0
A’B1
AB’2
AB3
0 1
0
1
A
B
Map Values
MODE 2
A’B’0
AB’2
A’B1
AB3
0 1
0
1
A
B
Map Values
![Page 4: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/4.jpg)
K Map-2 Variabel
Penyederhanaan K-map 2 Variabel
• 0 kotak terlingkupi = “0” (Low)
• 1 kotak terlingkupi = 2 variabel output
• 2 kotak terlingkupi = 1 variabel output
• 4 kotak terlingkupi = “1” (High)
• Melingkupinya harus posisi “Horisontal
“atau “vertikal” , yang dilingkupi digit ”1”
dan jumlah digit “1” yang dilingkupi 2n
(2,4,8,16, ...)
AB
A’B’
1 0
1
0 1
0
1
B
A
A
B’1 1
1
0 1
0
1
B
A
![Page 5: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/5.jpg)
Desain Pemetaan
K Map-2 Variabel
0 1
0
1
A
B
B’
B
A’ A
![Page 6: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/6.jpg)
Peta Karnaugh-2 Variabel
Contoh Kasus
0 1
1 0
0 1
0
1
B
A
F = AB’ + A’B
0 1
1 1
0 1
0
1
B
A
F = A’B + AB’ + AB
0 1
1 0
0 1
0
1
B
A
F = AB’ + A’B
0 1
1 1
0 1
0
1
B
A
F = A’B + AB’ + AB = A + B
![Page 7: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/7.jpg)
Peta Karnaugh-2 Variabel
Contoh Soal
• Tuliskan persamaan logika berdasarkan table kebenaran,
kemudian sederhanakan menggunakan K-map :
Map
ValuesA B Y
0 0 0 1
1 0 1 1
2 1 0 0
3 1 1 0
Map
ValuesA B Y
0 0 0 1
1 0 1 1
2 1 0 0
3 1 1 1
Sederhanakan persamaan logika berikut menggunakan K-map :
• Y = A + AB’ + A’B
• Y = B + AB’ + A’B
![Page 8: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/8.jpg)
Agenda
Chapter 1 – K-Map 2 Variabel
Chapter 2 – K-Map 3 Variabel
1. Model K-Map 3 Variabel
2. Desain Pemetaan K-Map 3 Variabel
Chapter 3 – K-Map 4 Variabel
Chapter 4 – Don’t Care
![Page 9: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/9.jpg)
Peta Karnaugh-3 Variabel
Map
ValuesA B C Y
0 0 0 0
1 0 0 1
2 0 1 0
3 0 1 1
4 1 0 0
5 1 0 1
6 1 1 0
7 1 1 1
Tabel Kebenaran
MODE 1
MODE 2
A’B’C’0
A’B’C1
A’BC3
A’BC’2
AB’C’4
AB’C5
ABC7
ABC’6
00 01 11 10
0
1
BC
A
A’B’C’0
A’BC’2
ABC’6
AB’C’4
A’B’C1
A’BC3
ABC7
AB’C5
00 01 11 10
0
1
AB
C
Map Values
![Page 10: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/10.jpg)
Desain Pemetaan
Peta Karnaugh-3 Variabel
MODE 1
00 01 11 10
0
1
BC
A
B’ B
A’
A
C
C’
![Page 11: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/11.jpg)
Desain Pemetaan
Peta Karnaugh-3 Variabel
MODE 2
00 01 11 10
0
1
AB
C
A’ A
C’
C
B
B’
![Page 12: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/12.jpg)
Peta Karnaugh-3 Variabel
Catatan Untuk K-map 3 Variabel
• 0 kotak terlingkupi = “0” (Low)
• 1 kotak terlingkupi = 3 variabel output
• 2 kotak terlingkupi = 2 variabel output
• 4 kotak terlingkupi = 1 variabel output
• 8 kotak terlingkupi = “1” (High)
• Melingkupinya harus posisi “Horisontal “atau
“vertikal” , yang dilingkupi digit ”1” dan jumlah
digit “1” yang dilingkupi 2n ( 2, 4, 8, ... )
1
1 1
00 01 11 10
0
1
BC
A
Y = AB’C’ + ABC + A’BC’
1 1
1 1
00 01 11 10
0
1
BC
A
1 1
1 1
00 01 11 10
0
1
BC
A
B C’
![Page 13: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/13.jpg)
Peta Karnaugh-3 Variabel
Map
ValuesA B C Y
0 0 0 0 0
1 0 0 1 1
2 0 1 0 1
3 0 1 1 0
4 1 0 0 1
5 1 0 1 1
6 1 1 0 1
7 1 1 1 1
0 1 0 1
1 1 1 1
00 01 11 10
0
1
BC
A
0 1 0 1
1 1 1 1
00 01 11 10
0
1
BC
A
Tabel Kebenaran
Y = AB’C’ + AB’C + ABC + ABC’ + A’B’C + A’BC’
Y = AB’C’ + AB’C + ABC + ABC’ + A’B’C + A’BC’
Y = A + B’C + BC’
![Page 14: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/14.jpg)
Peta Karnaugh-3 VariabelContoh Soal
• Sederhanakan persamaan logika yang didapat dari tabel
kebenaran berikut ini menggunakan K-map :
Map
ValuesA B C Y
0 0 0 0 0
1 0 0 1 1
2 0 1 0 0
3 0 1 1 1
4 1 0 0 1
5 1 0 1 1
6 1 1 0 0
7 1 1 1 1
Sederhanakan persamaan logika berikut menggunakan K-map :
• Y = A’BC + A’BC’ + ABC’ + ABC + AB’C
![Page 15: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/15.jpg)
Agenda
Chapter 1 – K-Map 2 Variabel
Chapter 2 – K-Map 3 Variabel
Chapter 3 – K-Map 4 Variabel
1. Model K-Map 4 Variabel
2. Desain Pemetaan K-Map 4 Variabel
![Page 16: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/16.jpg)
Peta Karnaugh-4 Variabel
Map
ValuesA B C D Y
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
10 1 0 1 0
11 1 0 1 1
12 1 1 0 0
13 1 1 0 1
14 1 1 1 0
15 1 1 1 1
A’B’C’D’0
A’B’C’D1
A’B’CD3
A’B’CD’2
A’BC’D’4
A’BC’D5
A’BCD7
A’BCD’6
ABC’D’12
ABC’D13
ABCD15
ABCD’14
AB’C’D’8
AB’C’D9
AB’CD11
AB’CD’10
00 01 11 10
00
01
11
10
CD
AB
A’B’C’D’0
A’BC’D’4
ABC’D’12
AB’C’D’8
A’B’C’D1
A’BC’D5
ABC’D13
AB’C’D9
A’B’CD3
A’BCD7
ABCD15
AB’CD11
A’B’CD’2
A’BCD’5
ABCD’14
AB’CD’10
00 01 11 10
00
01
11
10
AB
CD
MODE 1
MODE 2
![Page 17: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/17.jpg)
Peta Karnaugh-4 Variabel
00 01 11 10
00
01
11
10
CD
AB
Desain Pemetaan
MODE 1
BB’
A’
A
C’ C
D
D’
![Page 18: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/18.jpg)
Peta Karnaugh-4 Variabel
00 01 11 10
00
01
11
10
AB
CD
Desain Pemetaan
MODE 2
DD’
C’
C
A’ A
B
B’
![Page 19: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/19.jpg)
Peta Karnaugh-4 Variabel
Catatan Untuk K-map 4 Variabel
• 0 kotak terlingkupi = “0” (Low)
• 1 kotak terlingkupi = 4 variabel output
• 2 kotak terlingkupi = 3 variabel output
• 4 kotak terlingkupi = 2 variabel output
• 8 kotak terlingkupi = 1 variabel output
• 16 kotak terlingkupi = “1” (High)
• Melingkupinya harus posisi “Horisontal
“atau “vertikal” , yang dilingkupi digit ”1”
dan jumlah digit “1” yang dilingkupi 2n
(2, 4, 8, 16, ...)
1 1 1 1
1 1 1 1
1 1
1 1 1 1
00 01 11 10
00
01
11
10
ABCD
1 1
1 1
1
1
00 01 11 10
00
01
11
10
ABCD
A’ AC’ ACD’
B’C’
ABCD’A’BCD
![Page 20: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/20.jpg)
Contoh Soal 1
Sederhanakan persamaan logika berikut menggunakan K-map :
• Y = A′BC ′+ A′CD ′+ ABC + AB ′C′D ′+ ABC ′+ AB ′C
Peta Karnaugh-4 Variabel
![Page 21: Agendafahrudin.dosen.ittelkom-pwt.ac.id/.../04/7-Karnaugh-Map.pdfAgenda Chapter 1 –K-Map 2 Variabel 1. Model K-Map 2 Variabel 2. Desain Pemetaan K-Map 2 Variabel Chapter 2 –K-Map](https://reader030.vdocuments.net/reader030/viewer/2022013121/5d20832488c993ec448d3949/html5/thumbnails/21.jpg)
Peta Karnaugh-4 Variabel
Contoh Soal 2
• Sederhanakan persamaan logika yang
didapat dari tabel kebenaran berikut ini
menggunakan K-map :
Map
ValuesA B C D Y
0 0 0 0 0 0
1 0 0 0 1 0
2 0 0 1 0 1
3 0 0 1 1 1
4 0 1 0 0 0
5 0 1 0 1 0
6 0 1 1 0 1
7 0 1 1 1 1
8 1 0 0 0 0
9 1 0 0 1 1
10 1 0 1 0 0
11 1 0 1 1 1
12 1 1 0 0 1
13 1 1 0 1 0
14 1 1 1 0 0
15 1 1 1 1 0