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You are here:Open notes-->Seminar-topics-and-ppt-for-engineering-->Prime-Implicant

Prime Implicant## How to study this subject

A

prime implicantof a function is an implicant that cannot be covered by a more general (more reduced - meaning with fewer literals) implicant. W.V. Quine defined aprime implicantofFto be an implicant that is minimal - that is, the removal of any literal fromPresults in a non-implicant forF.Essential prime implicantsare prime implicants that cover an output of the function that no combination of other prime implicants is able to cover.Using the example above, one can easily see that while (and others) is a prime implicant, and are not. From the latter, multiple literals can be removed to make it prime:

The process of removing literals from a Boolean term is called

expandingthe term. Expanding by one literal doubles the number of input combinations for which the term is true (in binary Boolean algebra). Using the example function above, we may expand to or to without changing the cover ofThe sum of all prime implicants of a Boolean function is called its

complete sum,minimal covering sum, or Blake canonical form.## Official Notes

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