2-1 redundant addition with threshold logic

We investigate threshold based networks performing 2-1 addition using redundant binary operand representations. In particular we concern with establishing the networks with the smallest network depth assuming small weight and fan-in values. First we propose a depth-4 implementation and we show that the 2-1 addition can be computed by a threshold network with the size in the order of O(n) and with O(1) weight and fan-in values. Consequently, we prove that the network depth can be reduced to 2 and yet maintain the O(n) size and O(1) weight and fan-in asymptotic complexities.