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High-Precision Arithmetic
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
Figure 4.3 is a flowchart of BCD division. If the division operation is in the form z = x / y, then the algorithm can be described as follows: If the dividend is zero (x = 0) the quotient is zero.Division by zero is not defined, therefore a zero divisor (y = 0) is an invalid operation. In this case the first byte of the BCD result is set to FF hexadecimal. This special encoding is detected by the BCD conversion routines and handled as an invalid operand.If the elements x and y have equal signs, the quotient is positive. If they have unequal signs, the quotient is negative. This rule for the sign of the result is the same as the one used in the multiplication algorithm.The exponent of the quotient is the difference between the exponent of the dividend and the exponent of the divisor.The significand of the quotient is the significand of the dividend divided by the significand of the divisor.The operations performed on the significands may require adjusting the exponents in order to maintain a normalized result.
Errors in calculus
Published in Breach Mark, Essential Maths for Engineering and Construction, 2017
A quotient is where one expression is divided by another. When differentiating a quotient, the quotient rule is used. This rule says that if y=uv and u and v are both functions of x, then dydx=vdudx-udνdxv2.
Digital Logic, Arithmetic, and Conversions
Published in Julio Sanchez, Maria P. Canton, Microcontroller Programming, 2018
Julio Sanchez, Maria P. Canton
If multiplication can be reduced to repeated addition, then division can be conceptualized as repeated subtraction. In the case of division, the quotient (result) is the number of times the divisor must be subtracted from the dividend before zero or a negative value results from the subtraction. The flowchart in Figure 4-6 (in the following page) shows the logic steps in unsigned division.
Fully homomorphic encryption: a general framework and implementations
Published in International Journal of Parallel, Emergent and Distributed Systems, 2020
That is, Euclidean domains are integral domains in which division is possible. The elements q,r in condition 2. above are respectively called the quotient and the remainder of the division of a by b. It is important to observe that in a general Euclidean domain, quotient and remainder are not necessarily unique. This is the case if and only if the valuation ϕ satisfies the following additional condition: if a,b are two nonzero elements of A, then