pembahasan materi rangkaian logika quint mc cluskey

1. Quint Mc Clusky
Tugas 6 Rangkaian Logika

2. No 1
Fadl Lul Hakim Ihsan (34)

3. T (A,B,C,D,E) =  m ( 2, 3, 6, 7, 12, 13, 18, 22, 26, 28, 29 )
+ d ( 8, 14, 15, 19, 20, 23, 27, 30, 31)

4. 2 0 0 0 1 0
3 0 0 0 1 1
6 0 0 1 1 0
7 0 0 1 1 1
12 0 1 1 0 0
13 0 1 1 0 1
18 1 0 0 1 0
22 1 0 1 1 0
26 1 1 0 1 0
28 1 1 1 0 0
29 1 1 1 0 1
8 0 1 0 0 0
14 0 1 1 1 0
15 0 1 1 1 1
19 1 0 0 1 1
20 1 0 1 0 0
23 1 0 1 1 1
27 1 1 0 1 1
30 1 1 1 1 0
31 1 1 1 1 1
1
2
2
3
2
3
2
3
3
3
4
1
3
4
3
2
4
4
4
5
1. Ubah minterm menjadi
bentuk bilangan biner.
2. Tulis jumlah bit pada tiap
nilai minterm
don’t care

5. 0 0 0 1 0
0 1 0 0 0
0 0 0 1 1
0 0 1 1 0
0 1 1 0 0
1 0 0 1 0
1 0 1 0 0
0 0 1 1 1
0 1 1 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 0 0
0 1 1 1 0
1 0 0 1 1
1 1 1 0 1
0 1 1 1 1
1 0 1 1 1
1 1 0 1 1
1 1 1 1 0
1 1 1 1 1
1
2
3
4
5
0 0 0 1 -
0 0 - 1 0
- 0 0 1 0
0 1 - 0 0
0 0 - 1 1
- 0 0 1 1
0 0 1 1 -
- 0 1 1 0
0 - 1 1 0
0 1 1 0 -
- 1 1 0 0
0 1 1 - 0
0 0 1 1 -
1 0 1 - 0
0 - 1 1 1
- 0 1 1 1
- 1 1 0 1
0 1 1 - 1
1 0 1 1 -
1 - 1 1 0
2,3
2,6
2,18
8,12
3,7
3,8
6,7
6,22
6,14
12,13
12,18
12,14
18,19
20,22
7,15
7,23
13,29
13,15
22,23
22,30
1 1 0 1 -
1 1 - 1 0
1 1 1 0 -
1 1 1 - 0
0 1 1 1 -
- 1 1 1 0
1 0 - 1 1
1 - 0 1 1
1 1 1 - 1
- 1 1 1 1
1 - 1 1 1
1 1 - 1 1
1 1 1 1 -
26,27
26,30
28,29
28,30
14,15
14,30
19,23
19,27
29,31
15,31
23,31
27,31
30,31
1. Kelompokan
berdasarkan
jumlah bit.
2. Selanjutnya
kelompokan
minterm-minterm
yang memiliki
selisih hanya 1 bit
saja, gantikan
dengan tanda (-).
1 & 2
2 & 3
3 & 4
4 & 5

6. 0 0 0 1 -
0 0 - 1 0
- 0 0 1 0
0 1 - 0 0
0 0 - 1 1
- 0 0 1 1
0 0 1 1 -
- 0 1 1 0
0 - 1 1 0
0 1 1 0 -
- 1 1 0 0
0 1 1 - 0
0 0 1 1 -
1 0 1 - 0
0 - 1 1 1
- 0 1 1 1
- 1 1 0 1
0 1 1 - 1
1 0 1 1 -
1 - 1 1 0
2,3
2,6
2,18
8,12
3,7
3,8
6,7
6,22
6,14
12,13
12,18
12,14
18,19
20,22
7,15
7,23
13,29
13,15
22,23
22,30
1 1 0 1 -
1 1 - 1 0
1 1 1 0 -
1 1 1 - 0
0 1 1 1 -
- 1 1 1 0
1 0 - 1 1
1 - 0 1 1
1 1 1 - 1
- 1 1 1 1
1 - 1 1 1
1 1 - 1 1
1 1 1 1 -
26,27
26,30
28,29
28,30
14,15
14,30
19,23
19,27
29,31
15,31
23,31
27,31
30,31
*
*
0 0 - 1 -
- 0 0 1 -
- 0 - 1 0
- 0 - 1 1
- 0 1 1 -
0 - 1 1 -
- - 1 1 0
- 1 1 0 -
0 1 1 - -
- 1 1 - 0
1 0 - 1 -
1 - 0 1 -
- - 1 1 1
- 1 1 - 1
1 - 1 1 -
1 1 - 1 -
1 1 1 - -
- 1 1 1 -
1 - - 1
2,3,6,7
2,3,18,19
2,18,6,22
3,7,19,23
6,7,22,23
6,7,14,15
6,22,14,30
12,13,28,29
12,13,14,15
12,28,14,30
18,19,22,23
18,19,26,27
7,15,23,31
13,29,15,31
22,23,30,31
26,27,30,31
28,29,30,31
14,15,30,31
19,23,27,31
1. Selanjutnya
kelompokan lagi
gabungan minterm-
minterm yang memiliki
selisih hanya 1 bit saja,
gantikan dengan tanda
(-).
2. Beri tanda (*) untuk
gabungan minterm yang
tidak memiliki
pasangan.
dan seterusnya…

7. 0 0 - 1 -
- 0 0 1 -
- 0 - 1 0
- 0 - 1 1
- 0 1 1 -
0 - 1 1 -
- - 1 1 0
- 1 1 0 -
0 1 1 - -
- 1 1 - 0
1 0 - 1 -
1 - 0 1 -
- - 1 1 1
- 1 1 - 1
1 - 1 1 -
1 1 - 1 -
1 1 1 - -
- 1 1 1 -
1 - - 1
2,3,6,7
2,3,18,19
2,18,6,22
3,7,19,23
6,7,22,23
6,7,14,15
6,22,14,30
12,13,28,29
12,13,14,15
12,28,14,30
18,19,22,23
18,19,26,27
7,15,23,31
13,29,15,31
22,23,30,31
26,27,30,31
28,29,30,31
14,15,30,31
19,23,27,31
- 0 - 1 -
- - 1 1 -
- 1 1 - -
1 - - 1 -
2,3,6,7,18,19,22,23
6,7,22,23,14,15,30,31
12,13,28,29,14,15,30,31
18,19,26,27,22,23,30,31
*
*
Tulis yang bertanda (*) dari
pengelompokan sebelumnya
- 0 - 1 1
0 1 - 0 0
1 0 1 - 0
3,7,19,23
8,12
10,22
P
Q
R
S
T
U
V
1. kelompokan lagi
gabungan minterm-
minterm yang memiliki
selisih hanya 1 bit saja
hingga tidak dapat
digabungkan lagi,
gantikan dengan tanda
(-) pada selisih bit.
2. Beri tanda (*) untuk
gabungan minterm yang
sudah tidak memiliki
pasangan.
3. Namai Persamaan.
*
*
*
*
*
*
*

8. 2 3 6 7 12 13 18 22 26 28 29
P V V V V V V
Q V V V
R V V V V
S V V V
T V V
U V
V V
P P P P R R P P S R R
Maka Persamaannya :
P + R + S =
( - 0 - 1 - ) + ( - 1 1 - - ) + ( 1 - - 1 - ) = B D + B C + A D
1. Centang kolom
sesuai persamaan
2. Tandai jika pada
satu kolom hanya
terdapat 1 centang.
Pastikan persamaan
tersebut digunakan.
3. Arsir bagian baris
persamaan.
4. Arsir bagian kolom
yang tercentang
oleh persamaan
pada baris.

9. No 2
Didi Alfandi (33)

10. TABEL BINER
T (A,B,C,D,E) =  m ( 2, 3, 6, 7, 12, 13, 18, 22, 24, 28, 29 )
+ d ( 8, 14, 15, 19, 20, 23, 27, 30)
INDEKS 16 8 4 2 1 DIGIT
2 0 0 0 1 0 1
3 0 0 0 1 1 2
6 0 0 1 1 0 2
7 0 0 1 1 1 3
12 0 1 1 0 0 2
13 0 1 1 0 1 3
18 1 0 0 1 0 2
22 1 0 1 1 0 3
24 1 1 0 0 0 2
28 1 1 1 0 0 3
29 1 1 1 0 1 4
8 0 1 0 0 0 1
14 0 1 1 1 0 3
15 0 1 1 1 1 4
19 1 0 0 1 1 3
20 1 0 1 0 0 2
23 1 0 1 1 1 4
27 1 1 0 1 1 4
30 1 1 1 1 0 4

11. KELOMPOKKAN SESUAI JUMLAH BIT

12. INDEKS 16 8 4 2 1 DIGIT
2 0 0 0 1 0 1
3 0 0 0 1 1 2
6 0 0 1 1 0 2
7 0 0 1 1 1 3
12 0 1 1 0 0 2
13 0 1 1 0 1 3
18 1 0 0 1 0 2
22 1 0 1 1 0 3
24 1 1 0 0 0 2
28 1 1 1 0 0 3
29 1 1 1 0 1 4
8 0 1 0 0 0 1
14 0 1 1 1 0 3
15 0 1 1 1 1 4
19 1 0 0 1 1 3
20 1 0 1 0 0 2
23 1 0 1 1 1 4
27 1 1 0 1 1 4
30 1 1 1 1 0 4
1 2 : 0 0 0 1 0
8 : 0 1 0 0 0
-------------------------------
2 3 : 0 0 0 1 1
6 : 0 0 1 1 0
12 : 0 1 1 0 0
18 : 1 0 0 1 0
24 : 1 1 0 0 0
20 : 1 0 1 0 0
-------------------------------
3 7 : 0 0 1 1 1
13 : 0 1 1 0 1
14 : 0 1 1 1 0
19 : 1 0 0 1 1
22 : 1 0 1 1 0
28 : 1 1 1 0 0
-------------------------------
4 29 : 1 1 1 0 1
15 : 0 1 1 1 1
23 : 1 0 1 1 1
27 : 1 1 0 1 1
30 : 1 1 1 1 0
1 2 : 0 0 0 1 0
8 : 0 1 0 0 0
-------------------------------
2 3 : 0 0 0 1 1
6 : 0 0 1 1 0
12 : 0 1 1 0 0
18 : 1 0 0 1 0
24 : 1 1 0 0 0
20 : 1 0 1 0 0
-------------------------------
3 7 : 0 0 1 1 1
13 : 0 1 1 0 1
14 : 0 1 1 1 0
19 : 1 0 0 1 1
22 : 1 0 1 1 0
28 : 1 1 1 0 0
-------------------------------
4 29 : 1 1 1 0 1
15 : 0 1 1 1 1
23 : 1 0 1 1 1
27 : 1 1 0 1 1
30 : 1 1 1 1 0

13. 1 2 : 0 0 0 1 0
8 : 0 1 0 0 0
-------------------------------
2 3 : 0 0 0 1 1
6 : 0 0 1 1 0
12 : 0 1 1 0 0
18 : 1 0 0 1 0
24 : 1 1 0 0 0
20 : 1 0 1 0 0
-------------------------------
3 7 : 0 0 1 1 1
13 : 0 1 1 0 1
14 : 0 1 1 1 0
19 : 1 0 0 1 1
22 : 1 0 1 1 0
28 : 1 1 1 0 0
-------------------------------
4 29 : 1 1 1 0 1
15 : 0 1 1 1 1
23 : 1 0 1 1 1
27 : 1 1 0 1 1
30 : 1 1 1 1 0
1 2, 3 : 0 0 0 1 -
2, 6 : 0 0 - 1 0
2, 18 : - 0 0 1 0
8, 12 : 0 1 - 0 0
8, 24 : - 1 0 0 0
---------------------------------------
2 3, 7 : 0 0 - 1 1
3, 19 : - 0 0 1 1
6, 7 : 0 0 1 1 -
6, 14 : 0 - 1 1 0
6, 22 : - 0 1 1 0
12, 13 : 0 1 1 0 -
12, 14 : 0 1 1 - 0
12, 28 : - 1 1 0 0
18, 19 : 1 0 0 1 -
18, 22 : 1 0 - 1 0
20, 22 : 1 0 1 - 0
20, 28 : 1 - 1 0 0
24, 28 : 1 1 - 0 0
---------------------------------------
3 7,15 : 0 - 1 1 1
7, 23 : - 0 1 1 1
13, 15 : 0 1 1 - 1
13, 29 : - 1 1 0 1
14, 15 : 0 1 1 1 -
14, 30 : - 1 1 1 0
19, 23 : 1 0 - 1 1
19, 27 : 1 - 0 1 1
22, 23 : 1 0 1 1 -
22, 30 : 1 - 1 1 0
28, 29 : 1 1 1 0 -
28, 30 : 1 1 1 - 0
1 2, 3 : 0 0 0 1 -
2, 6 : 0 0 - 1 0
2, 18 : - 0 0 1 0
8, 12 : 0 1 - 0 0
8, 24 : - 1 0 0 0
---------------------------------------
2 3, 7 : 0 0 - 1 1
3, 19 : - 0 0 1 1
6, 7 : 0 0 1 1 -
6, 14 : 0 - 1 1 0
6, 22 : - 0 1 1 0
12, 13 : 0 1 1 0 -
12, 14 : 0 1 1 - 0
12, 28 : - 1 1 0 0
18, 19 : 1 0 0 1 -
18, 22 : 1 0 - 1 0
20, 22 : 1 0 1 - 0
20, 28 : 1 - 1 0 0
24, 28 : 1 1 - 0 0
---------------------------------------
3 7,15 : 0 - 1 1 1
7, 23 : - 0 1 1 1
13, 15 : 0 1 1 - 1
13, 29 : - 1 1 0 1
14, 15 : 0 1 1 1 -
14, 30 : - 1 1 1 0
19, 23 : 1 0 - 1 1
19, 27 : 1 - 0 1 1
22, 23 : 1 0 1 1 -
22, 30 : 1 - 1 1 0
28, 29 : 1 1 1 0 -
28, 30 : 1 1 1 - 0

14. 1 2, 3, 18, 19 : - 0 0 1 -
2, 6, 3, 7 : 0 0 - 1 -
2, 6, 18, 22 : - 0 - 1 0
8, 12, 24, 28 : - 1 - 0 0
-----------------------------------------------
2 3, 7, 19, 23 : - 0 - 1 1
6, 7, 14, 15 : 0 - 1 1 -
6, 7, 22, 23 : - 0 1 1 0
6, 14, 22, 30 : - - 1 1 0
6, 22, 7, 23 : - 0 1 1 -
12, 13, 14, 15 : 0 1 1 - -
12, 13, 28, 29 : - 1 1 0 -
12, 14, 28, 30 : - 1 1 - 0
18, 19, 22, 23 : 1 0 - 1 -
20, 22, 28, 30 : 1 - 1 - 0
1 2, 3 : 0 0 0 1 -
2, 6 : 0 0 - 1 0
2, 18 : - 0 0 1 0
8, 12 : 0 1 - 0 0
8, 24 : - 1 0 0 0
---------------------------------------
2 3, 7 : 0 0 - 1 1
3, 19 : - 0 0 1 1
6, 7 : 0 0 1 1 -
6, 14 : 0 - 1 1 0
6, 22 : - 0 1 1 0
12, 13 : 0 1 1 0 -
12, 14 : 0 1 1 - 0
12, 28 : - 1 1 0 0
18, 19 : 1 0 0 1 -
18, 22 : 1 0 - 1 0
20, 22 : 1 0 1 - 0
20, 28 : 1 - 1 0 0
24, 28 : 1 1 - 0 0
---------------------------------------
3 7,15 : 0 - 1 1 1
7, 23 : - 0 1 1 1
13, 15 : 0 1 1 - 1
13, 29 : - 1 1 0 1
14, 15 : 0 1 1 1 -
14, 30 : - 1 1 1 0
19, 23 : 1 0 - 1 1
19, 27 : 1 0 1 1
22, 23 : 1 0 1 1 -
22, 30 : 1 - 1 1 0
28, 29 : 1 1 1 0 -
28, 30 : 1 1 1 - 0
*
*
*
*
x
*
*
*
*
SAMA
*
*
*
*
*
JIKA SUDAH TIDAK BISA DIKELOMPOKKAN
MASUKKAN DALAM TABEL
x = DON’T CARE
* = ANGKAYANG SUDAH TIDAK BISA DIKELOMPOKKAN
1 2, 6, 3, 7, 18, 19, 22, 23 : - 0 - 1 - *

15. 2 3 6 7 12 13 18 22 24 28 29 MINTERM
2, 6, 3, 7, 18, 19 ,22, 23 A v v V v v v B'D
8, 12, 24, 28 B V V V A'CD
6,7,14,15 C V V CDE'
6, 14, 22, 30 D V V BD'E'
12, 13, 14, 15 E V V A'BC
12, 13, 28, 29 F V V V V BCD'
12, 14, 28, 30 G V V BCE'
20, 22, 28, 30 N V V ACE'
Maka diperoleh hasil
B’D + A’CD + BCD’
MASUKKAN ANGKA YANG DIBERI * PADA TABEL
V

16. No 3
Lusiana Diyan Ningrum (51)

17. Sederhanakan persamaan berikut dengan metode QUINE – Mc CLUSKEY
T(A, B, C, D, E) = ∑m ( 2, 3, 6, 7, 12, 13, 18, 22, 28, 29) +
d ( 8, 11, 14, 15, 19, 20, 23, 27, 30)

18. Indeks
A B C D E
(2) 0 0 0 1 0 1
(3) 0 0 0 1 1 2
(6) 0 0 1 1 0 2
(7) 0 0 1 1 1 3
(12) 0 1 1 0 0 2
(13) 0 1 1 0 1 3
(18) 1 0 0 1 0 2
(22) 1 0 1 1 0 3
(28) 1 1 1 0 0 3
(29) 1 1 1 0 1 4
Don’t care
Indeks
A B C D E
(8) 0 1 0 0 0 1
(11) 0 1 0 1 1 3
(14) 0 1 1 1 0 3
(15) 0 1 1 1 1 4
(19) 1 0 0 1 1 3
(20) 1 0 1 0 0 2
(23) 1 0 1 1 1 4
(27) 1 1 0 1 1 4
(30) 1 1 1 1 0 4

19. Q-M Method : Grouping minterms
indeks A B C D E
1 (2) 0 0 0 1 0
(8) 0 1 0 0 0 (don’t care)
2 (3) 0 0 0 1 1
(6) 0 0 1 1 0
(12) 0 1 1 0 0
(18) 1 0 0 1 0
(20) 1 0 1 0 0 (don’t care)
4 (15) 0 1 1 1 1 (don’t care)
(23) 1 0 1 1 1 (don’t care)
(27) 1 1 0 1 1 (don’t care)
(29) 1 1 1 0 1
(30) 1 1 1 1 0 (don’t care)
3 (7) 0 0 1 1 1
(11) 0 1 0 1 1 (don’t care)
(13) 0 1 1 0 1
(14) 0 1 1 1 0 (don’t care)
(19) 1 0 0 1 1
(20) 1 0 1 0 0 (don’t care)
(22) 1 0 1 1 0
(28) 1 1 1 0 0

20. indeks A B C D E
1 (2,3) 0 0 0 1 -
(2,6) 0 0 - 1 0
(2,18) - 0 0 1 0
(8,12) 0 1 – 0 0
2 (3,7) 0 0 - 1 1
(3,11) 0 - 0 1 1
(3,19) - 0 0 1 1
(6,7) 0 0 1 1 -
(6,14) 0 - 1 1 0
(12,13) 0 1 1 0 –
(12,14) 0 1 1 - 0
(18,19) 1 0 0 1 -
(20,22) 1 0 1 - 0
(20,28) 1 – 1 0 0
indeks A B C D E
3 (7,15) 0 - 1 1 1
(7,23) - 0 1 1 1
(11,15) 0 1 - 1 1
(11,27) - 1 0 1 0
(13,15) 0 1 1 - 1
(13,29) - 1 1 0 1
(14,15) 0 1 1 1 -
(14,30) – 1 1 1 0
(19,23) 1 0 – 1 1
(19,27) 1 – 0 1 1
(22,23) 1 0 1 1 -
(22,30) 1 – 1 1 0
(28,29) 1 1 1 0 -
(28,30) 1 1 1 - 0
























21. indeks A B C D E
1 (2,3,18,19) - 0 0 1 -
(2,3,6,7) 0 0 - 1 -
(2,6,3,7) 0 0 - 1 -
(2,18,3,19) - 0 0 1 -
2 (3,7,11,15) 0 - - 1 1
(3,7,19,23) - 0 - 1 1
(3,11,19,27) - - 0 1 1
(6,7,22,23) - 0 1 1 -
(6,7,14,15) 0 - 1 1 -
(6,14,22,30) - - 1 1 0
(12,13,28,29) - 1 1 0 -
(12,13,14,15) 0 1 1 - -
(12,14,13,15) 1 0 1 – 0
(12,14,28,30) - 1 1 - 0
(18,19,22,23) 1 0 - 1 -
(20,22,28,30) 1 – 1 - 0








22. indeks A B C D E
1 (2,3,18,19,6,7,22,23) - 0 - 1 -
2 sel : (13,29)
(19,23)
(19,27)
4 sel : (3,7,11,15)
(3,11,19,27)
(6,7,14,15)
(6,14,22,30)
(12,13,28,29)
(12,13,14,15)
(12,14,13,15)
(12,14,28,30)
(20,22,28,30)
8 sel : (2,3,18,19,6,7,22,23)
- 1 1 0 1 BCD’E
1 - 0 1 1
0 - - 1 1
- - 0 1 1
0 - 1 1 -
- - 1 1 0
- 1 1 0 -
0 1 1 - -
0 1 1 - -
- 1 1 - 0
1 - 1 - 0
1 0 - 1 1
- 0 - 1 -
AB’DE
AC’DE
A’DE
C’DE
A’CD
CDE’
BCD’
A’BC
A’BC
BCE’
ACE’
B’C

23. 2 3 6 7 12 13 18 22 28 29 11 14 15 19 20 23 27 30
(13,29) V V
(19,23) V V
(19,27) V V
(3,7,11,15) V V V V
(3,11,19,27) V V V V
(6,7,14,15) V V V V
(12,13,28,29) V V V V
(12,13,14,15) V V
(12,14,13,15) V V
(12,14,28,30) V V
(20,22,28,30) V V
(2,3,18,19,6,7,2
2,23)
V V V V V V
DON’T CARE

24. 2 3 6 7 12 13 18 22 28 29 11 14 15 19 20 23 27 30
(13,29) V V
(19,23) V V
(19,27) V V
(3,7,11,15) V V V V
(3,11,19,27) V V V V
(6,7,14,15) V V V V
(12,13,28,29) V V V V
(12,13,14,15) V V
(12,14,13,15) V V
(12,14,28,30) V V
(20,22,28,30) V V
(2,3,18,19,6,7,2
2,23)
V V V V V V
DON’T CARE

25. 2 3 6 7 12 13 18 22 28 29 11 14 15 19 20 23 27 30
(13,29) V V
(19,23) V V
(19,27) V V
(3,7,11,15) V V V V
(3,11,19,27) V V V V
(6,7,14,15) V V V V
(12,13,28,29) V V V V
(12,13,14,15) V V
(12,14,13,15) V V
(12,14,28,30) V V
(20,22,28,30) V V
(2,3,18,19,6,7,2
2,23)
V V V V V V
DON’T CARE

26. T(A,B,C,D,E) = ∑m ( 2, 3, 6, 7, 12, 13, 18, 22, 28, 29) +
d ( 8, 11, 14, 15, 19, 20, 23, 27, 30)
= (12,13,28,29) + (2,3,18,19,6,7,22,23)
= BCD + BC
Q-M Method Result