SOP/POS to Canonical SOP/POS

Canonical form of any expression (SOP/ POS) is the form where every minterm/ maxterm contains all the fundamental inputs.

We can convert any SOP/ POS expression to its canonical form by following method:

SOP Expression to Canonical SOP Expression:

To convert SOP to canonical SOP expression, let us understand by taking an example .

Let, F(A, B, C) = A'B + AB'C

  ANDing 1 to the minterm with missing input,

  A'B + AB'C = A'B.1 + AB'C               (property of 1)

                      = A'B.(C+C') + AB'C      (complementarity law)

                     = A'BC + A'BC' + AB'C  (distributive law)

now,

    F(A, B, C) = A'BC + A'BC' + AB'C

   hence converted to Canonical Form.

POS Expression to Canonical POS Expression:

To convert POS to canonical POS expression, let us understand by taking an example .

Let, F(A, B, C) = (A+B').(A+B'+C)

  ORing 0 to the maxterm with missing input,

  (A+B').(A+B'+C) = (A+B'+0).(A+B'+C)                       (property of 0)

                                = (A+B'+C.C').(A+B'+C)                 (complementarity law)

                                = (A+B'+C).(A+B'+C').(A+B'+C)   (distributive law)

                                = (A+B'+C).(A+B'+C).(A+B'+C')   (commutative law)

                                = (A+B'+C).(A+B'+C')                     (idempotence law)

now,

    F(A, B, C) = (A+B'+C).(A+B'+C')

   hence converted to Canonical Form.