Counting properties of the switch-tailed shift-registers
The properties of the switch-tailed shift registers as counters are examined. It is shown that the Hamming, distance between two successive states in a cycle is constant and equal to an odd number. An N-bit switch-tailed shift register has usually several cycles of period 2N. However, if N has odd divisors other than the unit then there exist cycles of period less than 2N. Actually it is shown that an N-bit switch-tailed shift register has a cycle of period P=2N/k iff k is an odd divisor of N. The number of cycles for each odd divisor of N are determined by a recursion formula.