Rational number operation unit for reduction

摘要

A rational number operation unit comprising division means which receives a rational number having numerator and denominator to be reduced for sequentially determining terms d1, d2, . . . of a continued fraction for the rational number or data S1, S2, . . . , the division means carrying out a first division for the numerator as a dividend and the denominator as a divisor, producing a quotient thereof as the first term d1 or the dependent data S1, carrying out a second division for a residue thereof as a new divisor and the divisor in the first division as a new dividend, producing a quotient thereof as the second term d2 or depending data S2, . . . , carrying out an (i+1)th division for a residue of the i-th division as a new divisor and the divisor in the i-th division as a new dividend, producing a quotient thereof as the term di+1 or depending data Si+1, calculation means responsive to the term di or depending data Si for calculating Pi=Pi-2+diPi-1 Qi=Qi-2+diQi-1 where Pi and Qi are numerator and denominator of an i-th approximate fraction of the rational number, and output means for determining if the residue of the division is zero, and outputting Pi/Qi of the i-th approximate fraction as a reduced result of the rational number when the residue is zero.