Signed-binary representations of integer k with symmetric digit set Dscrs - {-(2w - 1 ),-(2w-3),... ,-1,0,1,... ,2w - 3,2w - 1} may have lower weight than the unsigned-binary expansion of k. The "weight" is the number of nonzero digits in a binary expansion. Lower weight leads to fewer number of addition operations in the scalar multiplication, kP, of elliptic curve cryptosystems. Here P is a point on an elliptic curve. On the other hand, computing the minimum-weight signed-binary representation from left (most significant bit) to right (least significant bit) significantly reduces memory requirements because intermediate results do not need to be stored. Since the size of Dscrs is 2w + 1, a (w + 1)-bit data bus is necessary to represent the 2w + 1 elements in Dscr s. This is inefficient because a (w + 1)-bit bus is capable of denoting 2w+1 cases. We present a new signed-binary recoding algorithm with asymmetric digit set Dscra - {-(2w - 1),-(2w - 3),...,-1, 0,1,...,2w - 3}. For w = 2, our simulation results show that the average weight of signed-binary numbers with digit set {- 3,-1,0,1} is 0.285 times the length of their unsigned-binary expansions. For the optimal representations with {-1,0,1} the average ratio is 0.333. The number of additions is decreased by 14.4%. The encoding circuit requires 7 flip-flops and 22 gates to realize