This paper gives some theory and design of efficient binary block codes capable of correcting the deletion and/or insertion of the symbol "0" in a received sequence. This problem is shown to be equivalent to the efficient design of some L1 metric asymmetric error control codes over the natural alphabet, N. Optimal non-systematic and systematic code designs are given. In particular, given t in N, a recursive method is given to encode k in N information bits into a systematic code of length $n=k+tcdotlog_{2}k+O(loglog k)$, capable of correcting at most t deletions and/or insertions of 0's in every received word. Decoding can be efficiently performed by algebraic means with the Extended Euclidean Algorithm (EEA).