Question

A function F(A,B,C) defined by three Boolean variables A, B and C when expressed as sum of products is given by
$F=\overline{A}.\overline{B}.\overline{C}+\overline{A}.B.\overline{C}+A.\overline{B}.\overline{C}$
where, $\overline{A},\overline{B},and\overline{C}$ are the complements of the respective variables. The product of sums (POS) form of the function F is

• A. $F=(A+B+C).(A+\overline{B}+C).(\overline{A}+B+C)$
• B. $F=(\overline{A}+\overline{B}+\overline{C}).(\overline{A}+B+\overline{C}).(\overline{A}+\overline{B}+\overline{C})$
• C. $F=(A+B+\overline{C}).(A+\overline{B}+\overline{C}).(\overline{A}+B+\overline{C})(\overline{A}+\overline{B}+C)(\overline{A}+\overline{B}+\overline{C})$
• D. $F=(\overline{A}+\overline{B}+C).(\overline{A}+B+C).(A+\overline{B}+C).(A+B+\overline{C}).(A+B+C)$

Answer 1

The correct option is C $F=(A+B+\overline{C}).(A+\overline{B}+\overline{C}).(\overline{A}+B+\overline{C})(\overline{A}+\overline{B}+C)(\overline{A}+\overline{B}+\overline{C})$

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

$=\sum m(0,2,4)=\Pi M(1,3,5,6,7)$

$=(A+B+\overline{C}).(A+\overline{B}+\overline{C}).(\overline{A}+B+\overline{C}).(\overline{A}+\overline{B}+C).(\overline{A}+\overline{B}+\overline{C})$