There are two ways in which we can put the Boolean function. These ways are the minterm canonical form and maxterm canonical form.
A Literal signifies the Boolean variables including their complements. Such as B is a boolean variable and its complements are ~B or B', which are the literals.
The product of all literals, either with complement or without complement, is known as minterm.
Example:
The minterm for the Boolean variables A and B is:
A.B
A.~B
~A.B
The complement variables ~A and ~B can also be written as A' and B' respectively. Thus, we can write the minterm as:
A.B'
A'.B
Using variable values, we can write the minterms as:
Example:
Let's assume that we have three Boolean variables A, B, and C having values
A = 1
B = 0
C = 0
Now, we will take the complement of the variables B and C because these values are 0 and will take A without complement. So, the minterm will be:
Minterm=A.B'C'
Let's take another example in which we have two variables B and C having the value
B = 0
C = 1
Minterm = B'C
We know that, when Boolean variables are in the form of minterm, the variables will appear in the product. There are the following steps for getting the shorthand notation for minterm.
Example 1: Minterm = AB'
Example 2: Minterm = AB'C'
The sum of all literals, either with complement or without complement, is known as maxterm.
Example:
The maxterm for the Boolean variables A and B will be:
A+B
A+~B
~A+B
We know that the complement variables ~A and ~B can be written as A' and B' respectively. So, the above maxterm can be written as
A+B'
A'+B
Using the given variable values, we can write the maxterm as:
Example:
Let's assume that we have three Boolean variables A, B., and C having values
A = 1
B = 0
C = 0
Now, we will take the complement of the variables B and C because these values are 0 and will take A without complement. So, the maxterm will be:
Maxterm = A + B' + C'
Let's take another example in which we have two variables B and C having the value
B = 0
C = 1
Maxterm = B' + C
We know that, when Boolean variables are in the form of maxterm, the variables will appear in sum. The steps for the maxterm are same as minterm:
Let's take some example to understand the theory of shorthand notation
Example 1: Maxterm = A+B'
Example 2: Maxterm = A+B'+C'
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