"Swing" phenomenon

Let's sum up two equal numbers 5 + 5 represented in the ternary mirror-symmetrical number system:

It follows from this example that we have found the special addition case called the "swing". If the addition process goes on then starting from some step the process of the carry formation turns out to be repetitive and hence the addition becomes infinite. The "swing"-phenomenon is a variety of the "races" arising in digit automatons when elements are switching over.

To eliminate the "swing"-phenomenon one may use the following effective "technical" method. Let's delay the input signals of the single-digit adders with odd indices (k = ±1, ±3, ±5, ...) by one addition step. With this aim in mind only the adders with the even indices (k = 0, ±2, ±4, ...) form at the first addition step the intermediate sums and corresponding carries to the single-digit adders with the odd indices. At the second addition step the carries formed at the first step are summarized with the corresponding ternary variables of the odd digits of the summable numbers. Thanks to such an approach the "swing"-phenomenon is eliminated.

Let's demonstrate the above-considered method for the preceding example of adding 5+5:

The first step of the mirror-symmetrical addition is the carry formation from all the digits with the even indices (0, 2, -2). The adders of all digits with the odd indices (1, 3, -1, -3) do not operate at the first step. The second step is the addition of all carries arising at the first step with the ternary variables of the digits with the odd indices.