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Principal of duality and Demorgan’s theorems
Minterm, Sum of product, Maxterm and product of sum - Digital Electronics
11295    Arnab De    27/07/2019

### Minterm

A product term containing all the input variables of the function in either complemented or uncomplemented form is called a minterm. A 2-variables function has 22=4 possible minterms. If the inputs are A and B, then minterms are A’B’, A’B, AB’, AB. These products are called minterms or standard product or fundamental product. Each minterms are obtained by the AND operation of the inputs. The total minterms of a three input (A, B and C) functions are 23=8. This may be represented as m0, m1, m2, m3, m4, m5, m6, m7.  These are also known as minterm canonical form. The minterms combinations are given bellow,

 A B C Minterm Symbol 0 0 0 A’B’C’ m0 0 0 1 A’B’C m1 0 1 0 A’BC’ m2 0 1 1 A’BC m3 1 0 0 AB’C’ m4 1 0 1 AB’C m5 1 1 0 ABC’ m6 1 1 1 ABC m7

### Sum of Product

The sum of the minterms is known as sum of product. We can also express it into canonical form as below

### Maxterm

A sum term containing all the input variables of the function in either complemented or uncomplemented form is called a maxterm. A 2-variables function has 22=4 possible maxterms. If the inputs are A and B, then maxterms are A’+B’, A’+B, A+B’, A+B. Each minterms are obtained by the OR operation of the inputs. The total maxterms of a three input (A, B and C) functions are 23=8. This may be represented as M0, M1, M2, M3, M4, M5, M6, M7. These are also known as maxterm canonical form. The minterms combinations are given bellow,

 A B C Minterm Symbol 0 0 0 A’+B’+C’ M0 0 0 1 A’+B’+C M1 0 1 0 A’+B+C’ M2 0 1 1 A’+B+C M3 1 0 0 A+B’+C’ M4 1 0 1 A+B’+C M5 1 1 0 A+B+C’ M6 1 1 1 A+B+C M7

N.B. From that table, we found that complement of each maxterm is equal to the corresponding minterm. For examples: A+B+C is a maxterm. Its complement is (A+B+C)’. Now (A+B+C)’=A’B’C’ (by using demorgan’s theorems).

### Product of Sum

The product of the maxterms is known as product of sum. We can also express it into canonical form as below

Principal of duality and Demorgan’s theorems
Author Details
Arnab De
I have over 16 years of experience working as an IT professional, ranging from teaching at my own institute to being a computer faculty at different leading institute across Kolkata. I also work as a web developer and designer, having worked for renowned companies and brand. Through tutorialathome, I wish to share my years of knowledge with the readers.
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