In this paper we propose a novel efficient adaptive binary arithmetic coder which is multiplication-free and requires no look-up tables. To achieve this, we combine the probability estimation based on a virtual sliding window with the approximation of multiplication and the use of simple operations to calculate the next approximation after the encoding of each binary symbol. We show that in comparison with the M-coder the proposed algorithm provides comparable computational complexity, less memory footprint and bitrate savings from 0.5 to 2.3% on average for H.264/AVC standard and from 0.6 to 3.6% on average for HEVC standard.