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 2^{2}=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 2^{3}=8. This may be represented as m_{0}, m_{1}, m_{2}, m_{3}, m_{4}, m_{5}, m_{6}, m_{7. } 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’ |
m_{0} |
0 |
0 |
1 |
A’B’C |
m_{1} |
0 |
1 |
0 |
A’BC’ |
m_{2} |
0 |
1 |
1 |
A’BC |
m_{3} |
1 |
0 |
0 |
AB’C’ |
m_{4} |
1 |
0 |
1 |
AB’C |
m_{5} |
1 |
1 |
0 |
ABC’ |
m_{6} |
1 |
1 |
1 |
ABC |
m_{7} |
The sum of the minterms is known as sum of product. We can also express it into canonical form as below
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 2^{2}=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 2^{3}=8. This may be represented as M_{0}, M_{1}, M_{2}, M_{3}, M_{4}, M_{5}, M_{6}, M_{7. }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’ |
M_{0} |
0 |
0 |
1 |
A’+B’+C |
M_{1} |
0 |
1 |
0 |
A’+B+C’ |
M_{2} |
0 |
1 |
1 |
A’+B+C |
M_{3} |
1 |
0 |
0 |
A+B’+C’ |
M_{4} |
1 |
0 |
1 |
A+B’+C |
M_{5} |
1 |
1 |
0 |
A+B+C’ |
M_{6} |
1 |
1 |
1 |
A+B+C |
M_{7} |
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).
The product of the maxterms is known as product of sum. We can also express it into canonical form as below