ARITHMETIC UNIT FOR RATIONAL NUMBER

PURPOSE:To easily obtain the fraction reduction of a rational number or an approximate rational number by repeating the dividing of respective items to the rational number in which the fraction reduction should be executed and counting the approximate numerator and denominator for the rational number each time one item of a continued fraction is obtained. CONSTITUTION:A divider 211 divides respective items d1, d2,... to a rational number composed of the numerator and denominator in which the fraction reduction should be executed and calculates them repeatedly successively. Compound computing elements 221 and 231 to operate in parallel counts a numerator Pi and a denominator Qi of the approximate rational number for the rational number each time one item di of the continued fraction is obtained by the divider 211. The approximate rational number, when the development of the continued fraction is wholly executed, the number is coincident to the original rational number, and when the fraction reduction can be executed for the original rational number, the number is the one in which the fraction reduction is executed for the numerator and denominator of the original rational number. Consequently, when the fraction reduction cannot be executed for the original rational number, the continued fraction development is completed, simultaneously, an approximate rational number Pm/Wm obtained up to then is obtained as the fraction reduction result. When '1', '0' deciding circuits 260 and 270 detect the overshooting of the number of the digit of Pm and Qm before the development is completed, Pm-1 and Qm-1 obtained until then are immediately outputted as an approximate rational number.