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Avichal
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I have thought about it and every-time I think I have an answer I try to explain it to myself and I fail. I want an intuition behind it and if there is a proof better.
Thank you
Thank you
Oh okay, sorry if it was not clearStephen Tashi said:You might get an answer if you state the question clearly.
The sum of minterms and product of maxterms are two common methods used to represent boolean functions because they provide a systematic and structured way to express complex boolean expressions. These methods also allow for easy conversion between different representations, such as between truth tables and boolean expressions.
The sum of minterms and product of maxterms can be used to simplify boolean expressions and minimize the number of logic gates needed to implement a given circuit. This is because each term in the sum or product corresponds to a unique combination of inputs that can be represented by a single logic gate.
The sum of minterms is a boolean expression in which all possible minterms (i.e. rows) of a truth table that result in a 1 are ORed together. On the other hand, the product of maxterms is a boolean expression in which all possible maxterms (i.e. rows) that result in a 0 are ANDed together. In essence, the sum of minterms represents a boolean function in disjunctive normal form (DNF) while the product of maxterms represents a boolean function in conjunctive normal form (CNF).
The decision between using the sum of minterms or product of maxterms often depends on the given boolean expression and the desired outcome. In general, the sum of minterms is used to emphasize the 1s (true outputs) in a boolean expression, while the product of maxterms is used to emphasize the 0s (false outputs). The choice also depends on the ease of conversion between different representations and the simplicity of the final expression.
Yes, the sum of minterms and product of maxterms can be used interchangeably as they both represent the same boolean function. This is because any boolean function can be expressed in either DNF or CNF form, and therefore can be represented by either the sum of minterms or product of maxterms. The choice between the two is usually based on convenience and simplicity of representation.