Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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Patent•
27 Jul 1942
TL;DR: In this paper, the first two numbers of the dividend and the divisor are compared in a Wheatstone bridge circuit to obtain an approximate quotient and automatically operable means for testing and obtaining by means thereof a correct digit of the quotient.
Abstract: 571,270. Electrical calculating- apparatus. STANDARD TELEPHONES & CABLES, Ltd. July 27, 1943, No. 15048/44. Convention date, July 27, 1942. Divided out of 571,253. [Class 106 (i)] Electrically - operated calculating - apparatus adapted to perform division operations comprises means for entering a dividend and a divisor therein, automatically operable means for operating a Wheatstone bridge circuit to compare digits of the dividend with digits of the divisor to obtain an approximate quotient and automatically operable means for testing said approximate quotient and obtaining by means thereof a correct digit of the quotient. In the manner described in Specification 571,253 a machine performs addition, subtraction and multiplication from record cards under the control of manually set keys. Division.-The quotient is obtained digit-bydigit by comparing the first two numbers of the dividend and the divisor in a Wheatstone bridge circuit, Fig. 30, in which the resistance of the arm Q3-Q4 is diminished step-by-step until a relay Qr11 in the arm Q3-Q2 releases. This gives an approximate quotient and the corresponding partial product is deducted from the dividend. The approximate quotient is then tested before being punched in the card. The dividend is stored in the highest denomination storage relays possible and is transferred to solution switches SM10-17 (not shown). The decimal point in the quotient is placed according to the number of figures in the dividend before the point and the number in the divisor after the point, although some figures of the quotient may, of course, be zero. The perforator head commences to step with the sensing of the first significant figure of the divisor which is stored in the highest denomination of the storage relays. After the divisor is set up, the perforator head is arrested and addition relay Tr1 (not shown) operates to set up the divisor in the highest of the switches SM1-8, while the divisor is also retained in the storage relays. The D contacts of switches SM1-2 are connected to resistances QY1-18 representing in ohms the first two figures of the divisor. Similarly, resistances QY19-36 represent the first two figures of the dividend in SM10-11. Resistances QY37-45 having values 200, 300-900 ohms, are connected to the D contacts of switch QM1. When the bridge is unbalanced the relay Qr11 in the arm Q3-Q2 energizes to supply current to the stepping magnet QM1, so that brush D is caused to step round its contacts to reduce the resistance QY37-45 until the bridge is approximately balanced, when Qr11 releases and switch QM1 indicates the approximate quotient. The divisor on the storage relays.is then multiplied by the approximate quotient, and the 9's complement of first the lower partial product and then the higher partial product is transferred to the dividend over the C brush of switch TM2 wired in reverse from the B brush. If subtraction of the total partial product is possible, i.e. if the figure of the approximate quotient is sufficiently low, then carry over takes place on the switch SM10 at the complementary transfer of both the lower and the upper partial products, and both carry over impulses arrive in the quotient circuit Q. The calculator then checks to see whether or not one or more further subtractions are possible, in which case the figure of the quotient is appropriately increased. If one of the two carry over impulses is missing, the calculator initiates one or more additions until the missing impulse arrives, the quotient being correspondingly reduced. If both impulses arrive, QM2 advances two steps to position 3 and the transfer operation stops. A check is then made to determine whether the remainder of the dividend is less or more than the divisor. The dividend and divisor are connected to a potentiometer chain of resistances QY48-56, whereby if the divisor is higher than the corresponding denominations of the dividend a relay Qr13 operates. If Qr13 operates, QM2 advances to position 4 and the approximate quotient being proved, the appropriate perforation mechanism can be set up. QM2, QM1 then step round to normal position and the apparatus is ready for the calculation of the next figure. On the other hand, if Qr13 does not operate when QM2 readies position 3, the first figure of the remainder is equal to or higher than the first figure of the divisor and subtraction takes place. If the subtraction is possible, a carry over impulse from SM9 results and relay Qr7 operates, and the position of Qr13 is again checked. If Qr13 has operated, the punching mechanism is set up, suitably corrected. If Qr13 fails to operate after one subtraction when Qr7 has energized, then a further subtraction is necessary. If subtraction is not possible, no carry over results and Qr7 does not operate, and the divisor must be added back to the switches storing the dividend, whereupon Qr7 operates at carry over as before. If the approximate quotient is too high, SM9 produces only one carry over and QM1 is advanced to a lower figure as the divisor is added to the dividend switches until Qr7 received the missing carry over impulse. In this case, comparison by relay Qr13 is unnecessary. All the following digits of the quotient are found in the same way with suitable connections over brush E of TM3 to the carry over relays which are energized in turn for successive digits in a quotient of 9 figures, whereby first SM9, then SM10, and so on are put into circuit after SM17 for the estimation of the second, third and subsequent digits. The first carry over relay is energized for a tenth figure, the number of figures in the quotient being limited only by the dimensions of the card. After all the digits have been determined, punching takes place in known manner.
3 citations
Patent•
03 Jul 2013TL;DR: A quotient prediction circuit for division based on restoring division is presented in this paper, where the most significant digits of the intermediate remainder and most significant digit of a divisor are predicted.
Abstract: An arithmetic circuit for performing division based on restoring division includes an intermediate remainder register configured to store an intermediate remainder, a quotient prediction circuit configured to perform, based on information about two most significant digits of the intermediate remainder and a most significant digit of a divisor, quotient prediction having lower precision than a highest precision obtainable from the information, thereby generating a prediction result, a fixed-value multiplication circuit configured to output one or more N-th (N: integer) multiples of the divisor selected in response to the prediction result, one or more subtracters configured to subtract, from the intermediate remainder, the one or more N-th multiples of the divisor output from the fixed-value multiplication circuit, and a partial quotient calculating circuit configured to obtain a partial quotient in response to one or more carry-out bits of one or more subtractions performed by the one or more subtracters.
3 citations
TL;DR: In this article, it was shown that there exists a divisor f(x)=∑i=0deg(f)cixi of xn−1 for some n∈N such that ci=ni for 1≤i≤r.
3 citations
Patent•
24 Jun 1988
TL;DR: In this paper, the multiplicative inverse, A-1, of the original divisor, A, was found by computing a conversion factor, D, and then multiplying A by D to convert it to an element C, where C is also an element of a smaller Galois Field, GF(2M), which is a subfield of GF(22M).
Abstract: The invention is an apparatus and/or method which enables one to divide two elements, A and B, of GF(22M), that is, perform the operation B/A, by finding the multiplicative inverse of the divisor A, and then multiplying the inverse by the numerator, B. The multiplicative inverse, A-1, of A if found by computing a conversion factor, D, (100) and then multiplying A by D to convert it to an element C, (102) where C is also an element of a smaller Galois Field, GF(2M), which is a subfield of GF(22M). Specifically, C is equal to A2$(1,3)$+1, or A2$(1,3)$*A, in the field GF(22M). Next the multiplicative inverse, C-1, of C in GF(2M) is found by appropriately entering a stored look-up table containing the 2M elements of GF(2M), (104). The multiplicative inverse, C-1, of C is thereafter converted, by multiplying it by the conversion factor D calculated above, to the element of GF(22M) which is the multiplicative inverse, A-1, of the original divisor, A, (106). The multiplicative inverse, A-1, of A is then multiplied by B to calculate the quotient, B/A, (108).
3 citations
TL;DR: In this paper, it was shown that the singular subscheme of the union of the divisors in A has a primary decomposition where the primary components are supported on exactly the subvarieties which are blown up in the course of constructing the crepant resolution of the double cover.
3 citations