  We exhibit a family of neural networks of McCulloch and Pitts of size $2nk+2$
which can be simulated by a neural networks of Caianiello of size $2n+2$ and
memory length $k$. This simulation allows us to find again one of the result of
the following article: [Cycles exponentiels des r\'{e}seaux de Caianiello et
compteurs en arithm\'{e}tique redondante, Technique et Science Informatiques
Vol. 19, pages 985-1008] on the existence of neural networks of Caianiello of
size $2n+2$ and memory length $k$ which describes a cycle of length $k \times
2^{nk}$.
