FOR FREE CONTENT
Canonical form of SOP and POS
Canonical form of Sum of Product (SOP):
1. A product terms which contain each of 'n' variables as factors either in complement or uncomplemented form is called a minterm.
.png)
(Here each term contains all variables)
.png)
(Here each term contains all variables)
2. A minterm given the value "1" for exactly one combination of the variables.
3. The Sum of all minterms of 'f' for which 'f' assumes '1' is called canonical sum of products or disjunctive normal form.
Example:
Example of canonical minterms
| A | B | C | Y |
0 → 1 → 2 → 3 → 4 → 5 → 6 → 7 → | 0 0 0 0 1 1 1 1 | 0 0 1 1 0 0 1 1 | 0 1 0 1 0 1 0 1 | 1 0 1 0 0 1 0 1 |
.png)
.png)
Difference between SOP and canonical SOP:
In SOP each term contains one or more variables or literals but canonical SOP where each minterm have all variables.
.png)
(Here each term contains one or more variables)
.png)
(Here each term must contains all variables)
Canonical form of Product of Sum (POS):
1. Sum term which contains each of' 'n' variables as factors either in complemented and uncomplemented form is called a maxterm.
.png)
(Here each term contains all variables)
.png)
.png)
(Here each term contains all variables)
2. A maxterm gives the value '0' for exactly one combination of the variables.
3. The product of all maxterms of 'f' for which 'f' assumes '0' is called canonical Product of Sums or conjunctive normal form.
Example of canonical maxterms
| A | B | C | Y |
0 → 1 → 2 → 3 → 4 → 5 → 6 → 7 → | 0 0 0 0 1 1 1 1 | 0 0 1 1 0 0 1 1 | 0 1 0 1 0 1 0 1 | 1 0 1 0 0 1 0 1 |
.png)
.png)
Difference between POS and canonical POS:
In POS each term contains one or more variables or literals but canonical POS where each minterm must have all variables.
.png)
(Here each term contains one or more variables)
.png)
(Here each term must contains all variables)
Important:
From for three (3) variables Canonical SOP and POS we got:
.png)
.png)
Three variables have eight (8) combinations.
So, number of minterm of SOP form + number of maxterm is POS
.png)
.png)
How to calculate canonical SOP and POS:
| A | B | C | Y |
0 → 1 → 2 → 3 → 4 → 5 → 6 → 7 → | 0 0 0 0 1 1 1 1 | 0 0 1 1 0 0 1 1 | 0 1 0 1 0 1 0 1 | 1 0 1 0 0 1 0 1 |
From the above table if we calculate canonical SOP
.png)
Then definitely we can say rest of the output is -
.png)
