Find the base (−2) notation of an integer from its decimal notation (see Exercise).Exercis...

Find the base (−2) notation of an integer from its decimal notation (see Exercise).

Exercise

Show that if b is a negative integer less than − 1. then every nonzero integer n can be uniquely written in the form

where ak ≠ 0 and 0 ≤ aj < | b | for j = 0, 1, 2, … , k.We write n = (akak − 1 … a1 a0)b, just as we do for positive bases.