#### 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:

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

e.g. **F = A + B’C****F = 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

Read the full series at Part 1, Part 2, Part 3, Part 4, Part 5, Part 6 and Part 7.

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