## Q. 3.1

Convert the following expression into the standard SOP form.

$F=A+\bar{B} C$

## Verified Solution

The domain of this SOP expression is made up of A, B, and C.

In the first term, A, the other two variables B and C are absent. So the first term is multiplied by $B+\bar{B}$ and $C+\bar{C}$as below:

$A=A(B+\bar{B})(C+\bar{C} ) = ABC+AB\bar{C}+A\bar{B}C+A\bar{B}\bar{C}$

In the second term, BC, the variable A is absent. So the second term is multiplied by $A+\bar{A}$ as below:

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

The standard SOP form of the original expression is as follows:

$F=A+\bar{B} C=ABC+AB\bar{C} +A\bar{B} C+A\bar{B} \bar{C} +\bar{A} \bar{B} C=m_{1} +m_{4} +m_{5}+m_{6}+m_{7}=\sum{m(1,4,5,6,7)}$

where two same standard product terms $A\bar{B}C$ can be merged by using rule 7: A+A = A.