Advisor:  Prof. Amir Yehudayoff Abstract: In circuit complexity theory we classify Boolean functions according to the size of the Boolean circuits that computes them. We are going to talk about a new matrix rank called the "Blocky rank" which was defined not long ago and show how we can achieve a lower bound on the size of 2-depth circuit that computes a function f by finding lower bound on the Blocky rank. We will also discuss about general properties of this rank and computes the rank for a Linear threshold function, which is a basic operator in our circuits. The Inner product function was studied before in the context of circuit size and by using the blocky rank we improve the known result.