Minterm & SOP Expression

 Minterm (m):

Minterms are formed when binary inputs are connected using AND(.). They are denoted by "m".

example: A'.B, A.B'.C, A.B'.C'

SOP (Sum of Products) Expression:

SOP expressions are formed by connecting minterms using OR(+).

example: A'.B + A.B'.C + A.B'.C'.

Canonical SOP Expressions:

Canonical SOP expressions are those SOP expressions which contains all inputs in its every minterm.

example: A'.B.C + A.B'.C + A.B'.C'.

Cardinal (Function) Form of SOP Expression:

This is the function notation of a Canonical SOP expression using 𝚺 (Sigma).

example : F(A, B, C) = 𝚺 (0, 1, 2, 6).

This is done by writing the canonical SOP expression in its hexadecimal valued minterm.

example:  if the canonical SOP expression is A'.B.C + A.B'.C + A.B'.C' then its cardinal notation can be formed by:

            A'.B.C = 0.1.1 = m3

            A.B'.C = 1.0.1 = m5

            A.B'.C' = 1.0.0 = m4

    so,  F(A, B, C) = 𝚺 (3, 4, 5).