Explanation
Concept:
Canonical Form: Any Boolean function that expressed as a sum of minterms or as a product of max terms is said to
be in its canonical form.
There are two types of canonical forms:
SOP: Sum of products or sum of minterms
Example of SOP: XY + X’Y’
POS: Product of sums or product of max terms
Example of POS: (X+Y) (X’+Y’)
The max term expression will be formed by the terms which are not present in the min-term expression.
Example:
The logic expression given below is the minterm expression.
Y = Σm (0, 3, 6, 7, 10, 12, 15)
By converting the above min-term expression into max term expression, we get
Y = ΠM (1, 2, 4, 5, 8, 9, 11, 13, 14)
Calculation:
Given Boolean expression is,
[(x1+x2)(x3x4)]
By using Demorgan’s theorem, the above expression can be simplified as
</span><spanstyle="font−size:14pt;">=(x1+x2)+x3x4
=x1x2+x3x4
The K-map representation for the above expression is,
From the above K-map representation,
The number of minterms (sum of product terms) = 7
The number of variables (n) = 4
Total number of terms = 2n=24=16
The number of max terms (product of sum terms) = 16 - 7 = 9
