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Binary form of max-terms.

F (A,B,C,D) = $\pi$ M (0,2,3,6,7,8,9,12,13)

Step 1: Binary form of max-terms.

max-terms variables
- A B C D
---- ---- ---- ---- ---
0 0 0 0 0
2 0 0 1 0
3 0 0 1 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
12 1 1 0 0
13 1 1 0 1

Step 2: Grouping max terms according to number of 1's.

| Groups | Max-terms | variables | |----|----|----|

- - A B C D
0 0 0 0 0 0
1 2 0 0 1 0
8 1 0 0 0
2 3 0 0 1 1
6 0 1 1 0
9 1 0 0 1
12 1 1 0 0
3 7 0 1 1 1
13 1 1 0 1

Step 3: Combination of max-terms groups of two.

| Group | max-terms | variables | |----|----|----|

- - A B C D
1 (0,2) 0 0 _ 0
(0, 8 ) _ 0 0 0
2 (2,3) 0 0 1 _
(2,6) 0 _ 1 0
(8,9) 1 0 0 _
3 (3,7) 0 _ 1 1
(6,7) 0 1 1 _
(9, 13) 1 _ 0 1
(12,13) 1 1 0 _

Step 4: Combination of max-terms groups of four.

Group max-terms A B C D
1 (2,3,6,7) 0 _ 1 _
(2,6,3,7) 0 _ 1 _
(8,9,12,13) 1 _ 0 _
(8,12,9,13) 1 _ 0 _

Step 5: Prime Applicant table.

PI terms Decimal nos. 0 2 3 6 7 8 9 12 13
A + C 8,9,12,13 X (X) (X) (X)
A + B + D 0,2 X X
B + C + D 0,8 X X
A + C 2,3,6,7 X (X) (X) (X)