Binary-to-decimal conversion based on the divisibility of 28-1 by 5

The authors treat the case of converting a binary value, represented in the form of n bytes, into a decimal value, represented in the form of m BCD characters. The conversion, which is suitable for one-byte and two-byte processors, is based on the following observations: (a) 5 is a divisor of 2⁸-1 and 2¹⁶-1. (b) Modular binary arithmetic over 2^r-1 is easily performed. (c) Binary division by 2^r-1, in the case where the remainder is known to be zero, is easily performed. (d) All the prime factors of 2⁸-1 and 2¹⁶-1 are of the form 2^r-+1.