## Sum-of-Products Equations and Logic Circuits Assignment Help

Assignment Help: >> Karnaugh Map and Combinatorial Logic Design - Sum-of-Products Equations and Logic Circuits

Sum-of-Products Equations and Logic Circuits:

There are four possible technique to AND two input signals that are in the complemented and un-complemented 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 m0, m1, m2 and m3, where the suffix i of mi 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, m0, m1, m2, m3, m4, m5, m6 and m7 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. 