Conversion from Cardinal Form to Maxterm Expression
A maxterm expression can be obtained from a given boolean function in cardinal form by using the following steps:
- Convert maxterm designation into binary form keeping the total number of bits same as the number of variables used in the function.
- For 0 take the variable and for 1 take the complement of the variable.
- Add the variable and the complement for every bit to obtain the maxterm
- Multiply the maxterms to get maxterm expression.
Example:
Find the maxterm expression for the boolean function: F(A, B, C) = Î (7, 3)
Binary of 7 is 111: (A’ + B’ + C’)
Binary of 3 is 011: (A + B’ + C’)
Hence, Max Term expression: (A’ + B’ + C’)(A + B’ + C’)
Find the maxterm expression for the boolean function: F(A, B, C) = Î (0, 3, 5)
Binary of 0 is 000: (A + B + C)
Binary of 3 is 011: (A + B’ + C’)
Binary of 5 is 101: (A’ + B + C’)
Hence, Max Term expression: (A + B + C)(A + B’ + C’)(A’ + B + C’)
Conversion From Minterm Expression to Maxterm Expression
Minterm is the product of N distinct literals where each literal occurs exactly once. The output of the minterm functions is 1. Maxterm is the sum of N distinct literals where each literals occurs exactly once. The output of the maxterm functions is 0. The conversion from minterm to maxterm involves changing the representation of the function from a Sum of Products (SOP) to a Product of Sums (POS).
In this article, we will cover prerequisites like minterm, maxterm, minterm designation, maxterm designation, conversion from Cardinal form to Minterm Expression, and conversion from Cardinal form to Maxterm Expression with a detailed explanation of conversion from minterm expression to maxterm expression with solved examples and FAQs.