On the number of ones in outcome sequence of extended Pohl generator

Formulas for distributions of number of ones (non-zeroes) in the cycle of the output sequence of generalized binary Pohl generator are obtained. Limit theorems for these distributions are derived in the case when the lengths of registers are coprime and tend to infinity, the contents of different registers are independent, but cell contents within each register may be dependent. The consequences of these theorems are given for the case when the contents of cells are independent random variables having equiprobable distribution on $\{0,\,1\}$.