Question

The product of sum expression of a Boolean function $F(A,B,C)$ of three variables is given by $F(A+B+C)=(A+B+\overline{C}).(A+\overline{B}+\overline{C}).(\overline{A}+B+C).(\overline{A}+\overline{B}+\overline{C}).$ The canonical sum of product expression of $F(A,B,C)$ is given by

• A. $\overline{A}.\overline{B}C+\overline{A}BC+A\overline{B}.\overline{C}+ABC$
• B. $\overline{A}.\overline{B}.\overline{C}+\overline{A}B\overline{C}+A\overline{B}C+AB\overline{C}$
• C. $AB\overline{C}+A\overline{B}.\overline{C}+\overline{A}BC+\overline{A}.\overline{B}.\overline{C}$
• D. $\overline{A}.\overline{B}.\overline{C}+\overline{A}BC+AB\overline{C}+ABC$

Answer 1

The correct option is B $\overline{A}.\overline{B}.\overline{C}+\overline{A}B\overline{C}+A\overline{B}C+AB\overline{C}$

The function is given in POS form as,
$F=(A+B+\overline{C}).(A+\overline{B}+\overline{C}).(\overline{A}+B+C).(\overline{A}+\overline{B}+\overline{C})$

The above function can also be expressed as
$F(A,B,C)=\Pi M(1,3,4,7)$

The function can be expressed in SOP form as,
$F(A,B,C)=\sum m(0,2,5,6)$

$=\overline{A}.\overline{B}.\overline{C}+\overline{A}B\overline{C}+A\overline{B}C+AB\overline{C}$