SumofProducts Equations and Logic Circuits:
There are four possible technique to AND two input signals that are in the complemented and uncomplemented form ( A¯ B¯ , A¯ B, A B¯ , AB) also called as fundamental products.
Below table lists each fundamental product producing high outputs.
Table: Fundamental Products for Two Inputs
A

B

Fundamental
Product

Minterms

0

0

A B

m0

0

1

A B

m1

1

0

A B

m2

1

1

A B

m3

For example, A¯ B¯ is high when A are B are low. The fundamental products A¯ B¯ , A¯ B, A B¯ and AB are also represented by minterms m_{0}, m_{1}, m_{2} and m_{3}, where the suffix i of m_{i} comes from the decimal equivalent of the binary number. There lies the advantage of understanding binary numbers before we learn Sum of Products (SOP) methods. For 3 inputs A, B and C, there are 23 minterms, m_{0}, m_{1}, m_{2}, m_{3}, m_{4}, m_{5}, m_{6} and m_{7} as listed in Table.
Table: Fundamental Products for Three Inputs
A

B

C

Fundamental
Products

Minterms

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

For instance, when A = 1, B = 1, C = 0, the fundamental product results a high output for the case Y = A B C¯ = 110¯ = 1.