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Using a Karnaugh map, obtain the minimal sum-of-products form for these functions. a. F(A, B, C, D) = sigma m(0, 1, 3, 4, 5, 7, 8, 12) b. F(A, B, C, D) = sigma m(0, 2, 4, 5, 8, 10, 11, 12, 13) c. F(A, B, C, D) = sigma m(1, 2, 3, 5, 6, 9, 11, 13, 14, 15)
Expert Answer
| 1 | 1 | 1 | |
| 1 | 1 | 1 | |
| 1 | |||
| 1 |
Quad(0,4,12,8)=C’D’
Quad(0,1,4,5)=A’C’
Quad(1,3,5,7)=DA’
Hence the function (F)=C’D’+A’C’+DA’
……………………………………………………………………………………………………………………………………….
b.F(A,B,C,D)=(0,2,4,5,8,10,11,12,13)
| 1 | 1 | 1 | |
| 1 | 1 | ||
| 1 | 1 | ||
| 1 | 1 | 1 |
Quad(0,4,12,8)=C’D’
Quad(4,5,12,13)=C’B
Quad(3,2,11,10)=CB’
Hence The function F=C’D’+C’B+CB’
………………………………………………………………………………………………………………………………………….
c.F(A,B,C,D)=1,2,3,5,6,9,11,13,14,15)
| 1 | 1 | 1 | |
| 1 | |||
| 1 | 1 | 1 | |
| 1 | 1 |
Quad(13,15,9,11)=DA’
(1,3)=DA’B’
(2,6)=CD’A’
(6,.5)=BCD’
Hence the function F=DA’+DA’B’+A’CD’+BCD’
Note: give the index for the 4 rows i.e R1(0,1,3,2)
R2(4,5,7,6)
R3(12,13,15,14)
R4(8,9,11,10)
Now place 1 in the table as per the index order as above and form the quads and pairs,then write the sop equation.
