Question 3.15: Use a Karnaugh map to minimize the following standard SOP ex......
Use a Karnaugh map to minimize the following standard SOP expression:
F(A, B, C)=A\bar{C}+\bar{A}C+B\bar{C}+\bar{B}{C}The given SOP expression has a domain of three variables A, B, and C. You can map this SOP expression on a 3-variable Karnaugh map.
The product term A{\bar{C}} is mapped by placing 1s in the two cross cells between the row of A = 1 and the column of C = 0;
The product term \bar{A}{{C}} is mapped by placing 1s in two cross cells between the row of A = 0 and the column of C = 1;
The product term B{\bar{C}} is mapped by placing 1s in the two cross cells in the column of BC = 10;
The product term \bar{B}{{C}} is mapped by placing 1s in the two cross cells in the column of BC = 01.
After mapping the SOP expression in a Karnaugh map, you will turn to next step of grouping 1s.
The cells are grouped as shown in Figure 3.6.9.
Figure 3.6.9 shows two kinds of grouping method. Totally, there are at least three groups and each group of cells containing 1s creates one product term by eliminating the variables with different binary value and leaving the variables with the same binary value.
Add the three product terms and determine the resulting minimum SOP expression as follows:
The minimum SOP expression in Figure 3.6.9(a) is
The minimum SOP expression in Figure 3.6.9(b) is
F(A, B, C)={A}\bar{C}+\bar{B}C+\bar{A} {B}The above two SOP expressions are both minimized SOP expressions.
This illustrates that it is possible for you to get more than one result through Karnaugh map simplification.
