  We decide completely the cycle structure of pure summing register (PSR) and
complementary summing register (CSR). Based on the state diagram of CSR, we
derive an algorithm to generate de Bruijn cycles from CSR inspired by Tuvi
Etzion's publication in 1984. We then point out the limitation in
generalizations of extended representation we use in the algorithm proposed,
with a proof of the fact that only PSR and CSR contain pure cycles all dividing
n+1.
