Deriving SOP and POS

there are 2 canonical form of logical functions:

-          the Sum of Product, which represents AND;

-          the Product of Sum, representing OR.

Any Boolean function can be implemented in electronic form as a network of logic gates. Consider the following truth table:

We can express the function by itemizing and the combinations of A, B, and C that causes F to be 1.

Therefore,

F = A’BC’ + A’BC + ABC’ (SOP)

To derive F as a POS, simply apply de Morgan’s Law (compliment law)

Remember, de Morgan’s law states that

(a+ b )’ = a’b’;

a’b’ = a’ + b’;

F = A’BC’ + A’BC + ABC’ (SOP)

POS        = compliment of SOP

                = (SOP)’

                = (A’BC’ + A’BC + ABC’)’

                = AB’C + AB’C’ + A’B’C

POS = (A + B’ +C) x (A + b’ + C’) x (A’ + B’ +C)

Lua Xin Lin B031210345