Understanding Minterms and Maxterms In Digital Electronics – Karnaugh Map In Digital Electronics Tutorial Part 2

Understanding Minterms

A binary variable may appear in its normal form (as A) or in its complemented form (as A’). If we consider two variables such as A and B combined by an AND operation, then there are four possible combinations viz; A’B’, A’B, AB’ and AB. Each of these contain all the variables. These AND terms are called minterms or fundamental products or standard products.

Similarly for 3 binary variables such as A, B & C, there are 8 minterms – A’B’C’, A’B’C, A’BC’, AB’C’, A’BC, AB’C, ABC’ and ABC.

Thus, each minterm is obtained by ANDing all the variables with each variable being complemented if the bit is 0 and not complemented if bit is 1.

Below is the truth table for 3 variables:

Minterms Truth TableThus, whichever fundamental product is 1 i.e. present in F, it is known as Minterm.

e.g. F = A + B’CMinterms ExampleF = Σ(1,4,5,6,7)

The letters in parentheses list the binary variables, in the order that they appear in the truth table. The symbol Σ stands for the sum of the minterms that follow in the parentheses. The minterms that produce 1 for the function (F=A+B’C) are listed in their decimal equivalent. The minterms missing from the list are the ones that produce 0 for the function.

Understanding Maxterms

A function may be expressed as a product of sums or all the possible sum terms of these variables or their complements. A maxterm is a sum of all the variables within the logic system. The variable is complemented if bit is 1 and is not complemented if bit is 0. It is just the reverse of minterms.

Thus, each maxterm is the complement of the corresponding minterms.

e.g. if A’B’C’ is a minterms, then

(A’B’C’)’ = (A’)’ + (B’)’ + (C’)’ = A + B + C, which is a maxterm

Minterms and Maxterms in Digital ElectronicsRead the full series at Part 1, Part 2, Part 3, Part 4, Part 5, Part 6 and Part 7.

  1. მხოლოდ ამ საიტზე მხვდება თაკო ნაცვლიშვილის ფოტო რომელიც მიყურებს დამშეული თვალებით და ცდილობს რომ მომყიდოს პანდორას (რა ორიგინალური სახელია, ბრავო) იაფასიანი ბიჟუტერია მაშინ როდესაც ვცდილობ რომ ვისწავლო ლოგიკური წრედების იმპლემენტაციისთვის მნიშნელოვანი თეორია.

    ეს რა სამყაროში მოვხვდი. :(

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