Two concepts for new types of a magnetic domain wall based multiturn counter with true power on functionality are presented. Both counters use several closed loops of magnetic nanowires, each with different numbers of cusps. The turns are counted by the motion of domain walls through the loops, whereas a DW will move through on cusp during 90◦ external field rotation. Two concepts are introduced: a system based on binary logic, which is easy to integrate in digital electronics, and a system based on coprime numbers, which is useful to count large numbers. We have performed micromagnetic simulations in order to optimize the geometry of the cusp with respect to the operation margin of the device. Furthermore, the read-out scheme for both systems are shown.