## Q. 3.17

Use a Karnaugh map to minimize the following SOP expression:

$F(A, B, C, D) = \bar{A}\bar{B}\bar{C}+A\bar{C}\bar{D}+A\bar{B}+ABC\bar{D}+\bar{A}\bar{B}C$

## Verified Solution

Map the SOP expression on a 4-variable Karnaugh map. Notice that both groups exhibit “wrap around” adjacency. Figure 3.6.11 shows the simplification process. The group of eight cells is formed because the top and bottom cells are adjacent; the group of four cells is form to pick up the remaining two 1s because the cells in the outer columns are adjacent.

The resulting minimum SOP expression is

$F(A, B, C, D) =\bar{B}+A\bar{D}$