# Sum of Products and Product of Sum

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```					SOP & POS Form
Here you learn about the different forms in which an expression can be represented namely Canonical
form, Sum - of - Products(SOP) form and Product - of - Sum(POS) form.Along with this we will also discuss about
minterms and maxterms.

Canonical Form
A boolean expression having 'n' variables is said to be expressed in its canonical form when each term of the expression
contains all 'n' variables.

Example :
F(X , Y) = XY + XY'

But, F(A, B, C) = A'B'C + AB' + ABC' is not expressed in canonical form because the second term (i.e. AB') does not
contain C, the third variable present in F(A, B, C).

Sum - of - Product Form
Here each term of the expression consists of the product of various variables and then all those product terms are summed
up to represent the SOP form.

Example :
i) A.B + A'.B
ii) abc + a'bc + a'b'c

Product - of - Sum Form
Here each term of the expression consists of the sum of various variables. The product of all the summed up terms gives us
the POS expression.

Example :
i) (X + Y).(X' + Y)
ii) (a + b + c).(a + b' + c).(a' + b' + c)

Minterm
A term in the SOP expression which contains all 'n' variables present in the expression is known as
minterm.

Maxterm
A term in the POS expression which contains all 'n' variables present in the expression is known as
maxterm.

Examples
First of all we need to construct the truth table.
1. Find the SOP expression for F(A, B, C) = Σ(0, 2, 3, 7)

Solution :
Therefore the SOP expression is = A'B'C' + A'BC' + A'BC + ABC

2. Find the POS expression for F(x, y, z) = Π(1, 4, 5, 7)

Solution :
First of all we need to construct the truth table.

Therefore the POS expression is = (A + B + C).(A' + B + C).(A' + B + C').(A' + B' + C')

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Description: This document deals with the various representation forms of an expression in boolean algebra i.e. sum of products and product of sum. Examples are mentioned to improve your understanding.