This paper describes design of a low-complexity algorithm for adaptive encoding/ decoding of binary sequences produced by memoryless sources. The algorithm implements universal block codes constructed for a set of contexts identified by the numbers of non-zero bits in previous bits in a sequence. We derive a precise formula for asymptotic redundancy of such codes, which refines previous well-known estimate by Krichevsky and Trofimov, and provide experimental verification of this result. In our experimental study we also compare our implementation with existing binary adaptive encoders, such as JBIG's Q-coder, and MPEG AVC (ITU-T H.264)'s CABAC algorithms.