| 摘要 |
A plurality of modular arrays, each structured from a common module, are connected together so as to form a binary quotient by successive approximations. For divisors that fall into that group of numbers that have reciprocals with a reasonably short period, the forming of a quotient with such a divisor and any dividend can be greatly accelerated after the add and shift sequence for the first period of the divisor reciprocal is obtained. A unity array, divisor array, dividend array, and quotient array may all be of equal length, but must be longer than the length of the periods of the reciprocals of the divisors utilized. The reciprocal of the divisor is effectively formed in the divisor array by generating a shift and add sequence that will produce a product that is a series of binary ones. After the first period of the divisor reciprocal is formed, the binary bits of the reciprocal start to repeat for the second period, and so on. By using the formed shift and add sequence that effectively represents the reciprocal of the divisor for a single period, to manipulate the dividend, the dividend is effectively multiplied by the reciprocal of the divisor, producing a product, most significant bit first, that is the quotient of the dividend and divisor. After obtaining the shift and add sequence representative of the first period of the divisor reciprocal, the quotient has been formed, most significant bit first, to a precision equal to the number of bits in the first period of the divisor reciprocal. The precision of the quotient can now be doubled by adding the formed quotient with itself after the quotient addend is shifted to the right the number of bit positions to which the quotient is precise. At the next step, the quotient precision can be quadrupled, and so on.
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