Canonical and Standard form of POS (with examples)
This video is about the Canonical and Standard forms of POS Boolean expressions.
A Boolean expression is a logical statement that can either be TRUE or FALSE. Examples of Boolean expressions are:
A + BC; AB + AB' + A'B; (A+B)(B+C)(A+B')
Every Boolean expression can be represented in two forms: SOP form or POS form.
Boolean Algebra playlist: • Boolean Algebra
Canonical and Standard form of SOP: • Canonical and Standard form of SOP (w...
SOP Boolean expression can either be in its
Canonical form, or
Standard form
Similarly, POS Boolean expression can either be in its
Canonical form, or
Standard form
This video will help you understand how to identify each of these representations and how to make conversions between them.
POS stands for Product of Sums or product of maxterms. The POS expression multiplies up the maxterms to form a Boolean expression.
This video explains the method for deriving an POS Boolean expression from a given truth table.
Always remember, for POS, if the value of the input variable is 1, the minterm will have the complement of the variable. If the value of the variable is 0, the minterm will have the literal as such. This is just the opposite to that of a SOP expression.
An POS Boolean expression can be written as
F = (X + Y + Z)(X + Y + Z’)(X + Y’ + Z’)
(or)
F =M0 . M1 . M3
(or)
F = πM(0,1,3)
A POS expression is said to be in its canonical form if each sum term in the expression contains all the literals involved.
A POS expression is said to be in its standard form if each sum term in the expression does not contain all the literals involved. Standard POS is also known as Minimal POS or Non-canonical form of POS.
A canonical POS expression can be simplified using some Boolean laws to obtain the standard POS expression.
This video also explains the simple step by step procedure for converting a standard POS expression into its Canonical form.
Watch this video until the end to easily understand the Product of sums Boolean expressions.
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