Mathematical Expression for multiplication and addition of binary arrays

Question

Assuming I have two binar arrays with 3 bits. Array A = 1,1,0 and Array B = 0,1,1. Now I want to perform bit-wise AND operation (or you can say multiplying) between A and B and then add the bits of the resultant array. For the above example the result will be: (1*0) + (1*1) + (0*1) = 1.

How can mathematical express this which will look good enough to put in a research paper?

Answer 1

You cab define the bits of $A$ as $a_i$ then write $\sum_ia_ib_i$