Canonical and Standard form of SOP (with examples)
This video is about the Canonical and Standard forms of SOP 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
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.
SOP stands for Sum of Products or sum of minterms. The SOP expression sums up minterms to form a Boolean expression.
This video explains the method for deriving an SOP Boolean expression from a given truth table.
Always remember, for SOP, if the value of the input variable is 0, the minterm will have the complement of the variable. If the value of the variable is 1, the minterm will have the literal as such.
An SOP Boolean expression can be written as
F = A'B'C + AB'C' + ABC' + ABC
(or)
F = m1 + m4 + m6 + m7
(or)
F = ∑m(1,4,6,7)
An SOP expression is said to be in its canonical form if each product term in the expression contains all the literals involved.
An SOP expression is said to be in its standard form if each product term in the expression does not contain all the literals involved. Standard SOP is also known as Minimal SOP or Non-canonical form of SOP.
A canonical SOP expression can be simplified using some Boolean laws to obtain the standard SOP expression.
This video also explains the simple step by step procedure for converting a standard SOP expression into its Canonical form.
Watch this video until the end to easily understand the Sum of Products Boolean expressions.
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