Question 3.12: Map the following SOP expression on a Karnaugh map: F(A, B, ......
Map the following SOP expression on a Karnaugh map:
F (A,B,C)=B{\bar{C}}One method is to convert this nonstandard SOP expression into a standard SOP expression firstly.
F(A,B,C)=B{\bar{C}}=({\bar{A}}+A)B{\bar{C}}={\bar{A}}B{\bar{C}}+A B{\bar{C}}=m_{2}+m_{6}Since m_{2}\operatorname{and}m_{6} are in the standard SOP expression, their corresponding cells are placed 1s and the other cells are placed 0s on Karnaugh map. The mapping result is shown in Figure 3.6.4.
Another method is to directly map the product term, B{\bar{C}} , on a Karnaugh map.
Product term B{\bar{C}} is not a minterm due to the absence of a variable A. You can multiply it by {\bar{A}}+A and convert it into two minterms, m_{2} and m_{6} . The binary value of B{\bar{C}} is 10 which corresponds to the column of 10 on a Karnaugh map. m_{2} is located at the cross cell between the row of A = 0 and the column of BC = 10; m_{6} is located at the cross cell between the row of A = 1 and the column of BC = 10. This means that the product term, B{\bar{C}}, can be mapped directly by placing 1s on the cross cells between the column of BC = 10 and the row of A = 0 and A = 1, which actually places 1s on the two cells corresponding to the column of BC = 10. Therefore, you can directly map the product term on a Karnaugh map.
