U.S. Pat. No. 4,652,856 (Mohiuddin et al.) discloses a multiplication-free multi-alphabet arithmetic code in which each sub-interval is stored in floating point format, as explained above, such that the mantissa stored within the A register is a binary fraction greater than 0.1. In accordance with the approximation proposed by Mohiuddin, a variable criterion is adopted which either truncates the mantissa of the sub-interval to exactly 0.1 (binary) or, alternatively, rounds it up to 1. Such an approximation still achieves the desired compression, but at a loss of efficiency. In other words, more bits than the minimum are required for representing the compressed data string. The inefficiency associated with Mohiuddin's procedure depends on the nature of the source data being compressed