The central topic of this paper is the
alternating greedy expansion of integers, which is defined to be a binary
expansion with digits
{0,±1} with the property that the nonzero digits have alternating signs. We collect known results about this alternating
greedy expansion and complement it with other useful properties and algorithms. In the second part, we apply it to give an algorithm for computing a joint
expansion of
d integers of minimal joint Hamming weight from left to right, i.e., from the column with the most significant bits towards the column with the least significant bits. Furthermore, we also compute an
expansion equivalent to the so-called
w-NAF from left to right using the alternating
greedy expansion.