a coding system comprises the comparing circuit which compares a magnitude of the range on the number line which is allocated to the most probability symbol with a magnitude of the fixed range on the number line which is allocated to the less probability symbol . if the range allocated to the mps is smaller than that to the lps , and when the symbol is the mps , the range allocated to the lps is generated . if the range allocated to the mps is smaller than that to the lps , and when the symbol is the lps , the range allocated to the mps is generated . by the system , a coding efficiency is improved especially when a probability of occurrence of lps is approximate to 1 / 2 .