WO2016047848A1

WO2016047848A1 - Apparatus and method for calculating remainder

Info

Publication number: WO2016047848A1
Application number: PCT/KR2014/010326
Authority: WO
Inventors: 정석원
Original assignee: (주)셀로직
Priority date: 2014-09-24
Filing date: 2014-10-31
Publication date: 2016-03-31
Also published as: KR20160035882A

Abstract

The present invention relates to an apparatus for calculating a remainder, the apparatus, which calculates the remainder of dividing the result of a subtraction of two integers by a prime number, comprising: a first conversion unit and a second conversion unit for receiving input of a first integer and a second integer and converting same into a first binary number and a second binary number of n bits, respectively; a first addition unit for summing a binary complement of the second binary number, the first binary number and 1; a second addition unit for summing the reference integers determined in accordance with the second binary number and prime number; a third addition unit for summing the binary complement of the resulting sum of the second addition unit, the first binary number and 1; a control unit for selecting one from among the resulting sum of the first addition unit and the resulting sum of the third addition unit on the basis of the size of first integer and second integer, wherein if the first integer is equal to or greater than the second integer, then concluding the binary number of n bits contained in the resulting sum of the first addition unit as the remainder of dividing the result of the subtraction of first and second integers by the prime number.

Description

Apparatus and method for calculating the remainder

The present invention relates to an apparatus for calculating a remainder and a method thereof, and more particularly, an apparatus for calculating a remainder for simply implementing a remainder on hardware by dividing a subtraction result of any two integers by a prime number. And to a method thereof.

Conventional arithmetic logic units (ALUs) perform not only addition operations based on adders, but also various arithmetic operations, such as subtraction operations, and various logical operations such as OR and OR.

Among them, the division operation means the division of a number by another number by the inverse of the multiplication, and is also called a manufacturing method or division. At this time, the divided number is the dividend, the divided number is the divisor, the answer is the quotient, and the remainder that is not divided is called the remainder.

The division is divided into equal parts that divide the dividend into numbers representing the divisor and inclusion agents indicating how many divisors are included in the dividend.

In division, the distribution law does not hold, but in general, a ÷ b ÷ c = a ÷ c ÷ b = a ÷ (b × c), and a ÷ b = (a × c) ÷ (b × c) = ( a ÷ c) ÷ (b ÷ c) is also established.

In addition, when dividend and divisor have 0, 0 ÷ a = 0 (a ≠ 0), the quotient of 0 ÷ 0 is negative, and a ÷ 0 is disabled.

Prior art related to the present invention is Republic of Korea Patent Publication No. 10-1997-0059919 (published Aug. 12, 1997, the title of the invention: the remaining calculation method and circuit).

Prime number means a positive integer greater than 1 divided by 1 and itself, and 2, 3, 5, 7, 11, 13, 17, 19, and so on.

In this case, for any two integers having a value less than a decimal, when the remainder of subtracting two integers divided by a decimal number, the two subtraction results are different from each other if the result is greater than zero or less than zero. Do.

Therefore, in the related art, when calculating a remainder obtained by subtracting a result of an arbitrary two integers divided by a decimal number, a case relation of two arbitrary integers is first determined, and the remainder is calculated in different ways according to the determination result.

As such, in the related art, since a process of deciding which two integers are to be subtracted first and which method is to be calculated according to the result has to be performed first, it takes a long time for the calculation result to be derived and it is necessary to shorten it.

SUMMARY OF THE INVENTION The present invention has been made in accordance with the above-described needs, and provides an apparatus and method for calculating the remainder for simplifying the hardware division of the result of subtracting any two integers into prime numbers. There is a purpose.

An apparatus for calculating a remainder according to an aspect of the present invention is an apparatus for calculating a remainder obtained by dividing a result of subtraction of two integers by a prime number, and receiving a first integer and a second integer, respectively, each having an n-bit first A first converting unit and a second converting unit converting the binary number and the second binary number; A first adder configured to add the first binary number and the first binary number to which the second binary number is complemented; A second adder configured to add the second binary number and a reference integer determined corresponding to the decimal number; A third adder configured to add the first binary number and the first binary number to which the complementary result of the sum of the second adder is processed; And selecting a sum result of the first adder or a sum result of the third adder based on the magnitudes of the first and second integers, and wherein the first adder is greater than or equal to the second integer. And a control unit for determining the n-bit binary number included in the negative sum result as the remainder obtained by dividing the subtraction result of the first and second integers by a decimal number.

The present invention may further include a first repair processing unit for repairing the second binary number and a second repair processing unit for repairing the sum result of the second addition unit.

In the present invention, the reference constant is set to t when the decimal is represented by 2 ⁿ -t.

In the present invention, if the first integer is less than the second integer, the control unit determines that n-bit binary numbers included in the sum result of the third adder is the remainder of dividing the difference between the first integer and the second integer by a fraction. It is characterized by.

In the present invention, the control unit determines that the first integer is greater than or equal to the second integer when the (n + 1) -th bit included in the sum of the first adder is 1, and (n + 1) included in the sum result. If the) th bit is 0, the first integer is determined to be less than the second integer.

According to an aspect of the present invention, there is provided a system comprising: a third conversion unit converting a binary number to a decimal number determined by the control unit by dividing the difference between the first integer and the second integer by a decimal number; And an output unit for outputting a decimal number converted by the third conversion unit.

According to an aspect of the present invention, there is provided a method for calculating a remainder obtained by dividing a result of subtraction of two integers by a prime number, wherein the first transform unit and the second transform unit include a first integer and a second integer. Receiving and converting the n-bit first and second binary numbers, respectively; Adding a first binary addition and a complementary binary number by the first addition unit to the first binary number and 1; Summing a second integer and a reference integer determined in correspondence with the decimal part; Adding a third binary addition-complementary binary number, the first binary number and the first one, of which the complementary result of the second addition unit is added; And determining, by the controller, a result of dividing the subtraction result of the first integer and the second integer by a decimal number based on the magnitude of the first and second integers, wherein the controller is configured to determine the first integer. In the case of two or more integers, the n-bit binary number included in the sum result of the first addition unit may be determined as the remainder obtained by dividing the subtraction result of the first and second integers by a decimal number.

In the determining of a result of dividing the difference between the first integer and the second integer by a fraction, the control unit, if the first integer is less than the second integer, n bits included in the sum result of the third adder The binary number of is determined as the remainder obtained by dividing the difference between the first integer and the second integer by a decimal number.

In the step of summing the second binary number of the present invention and a reference constant determined corresponding to the decimal point, the reference integer may be set to t when the decimal point is expressed as 2 ⁿ -t.

In the determining of the remainder obtained by dividing the subtraction result of the first integer and the second integer by a decimal number, the control unit may determine that the (n + 1) -th bit included in the sum result of the first adder is 1; It is determined that one integer is greater than or equal to the second integer, and if the (n + 1) -th bit included in the sum result is 0, the first integer is determined to be less than the second integer.

According to the present invention, after determining the remainder obtained by subtracting the subtraction result of the first integer and the second integer by a decimal number, the third conversion unit uses a decimal number determined by the remainder of the subtraction result of the subtraction of the first and second integers by a decimal number. Converting to; And an output unit outputting the converted decimal number.

According to the present invention, the remainder obtained by subtracting the result of subtraction of two integers by a plurality of addition units regardless of the magnitude relationship between two integers, and after subtracting the result of subtraction of two integers by a decimal number according to the magnitude relationship of two integers By determining, we can compute the remainder faster.

In addition, the present invention can simply determine the magnitude relationship between two integers by checking the most significant bit included in the sum result.

1 is a block diagram of an apparatus for calculating a remainder according to an embodiment of the present invention.

2 is a flowchart illustrating an implementation process of a method of calculating a remainder according to an embodiment of the present invention.

Hereinafter, an apparatus and method for calculating a remainder according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings. In this process, the thickness of the lines or the size of the components shown in the drawings may be exaggerated for clarity and convenience of description. In addition, terms to be described below are terms defined in consideration of functions in the present invention, which may vary according to the intention or convention of a user or an operator. Therefore, definitions of these terms should be made based on the contents throughout the specification.

Referring to FIG. 1, an apparatus for calculating a remainder according to an embodiment of the present invention includes a first converter 10, a second converter 20, a first adder 40, and a second adder 50. And a third adder 60 and a controller 70.

Specifically, in the present embodiment, the remainder obtained by dividing the result of subtraction of two integers (U, V) by a prime number is calculated, but the relationship between the decimal and the two integers is expressed by Equation 1 below.

Equation 1

That is, in the present embodiment, in order to easily calculate the remainder obtained by subtracting the result of subtraction of two integers each smaller than the decimal, the first transform unit 10 and the second transform unit 20 convert the first integer and the second integer. It receives the input and converts the n-bit first binary number and the second binary number, respectively.

In the present embodiment, n bits means a bit set composed of n bits, and includes the first bit to the nth bit, the first bit corresponds to 2 ⁰ , and the nth bit corresponds to 2 ^n-1 . Let's define.

In addition, the first integer and the second integer, or the first binary number and the second binary number are freely determined according to the input order, and 1 or 2 may simply be an identifier for distinguishing two integers.

Hereinafter, an example of calculating a remainder obtained by dividing a number by subtracting a second integer from a first integer by a decimal number will be described.

Decimals are positive integers greater than 1, dividing by 1 and themselves, so they can be represented as 2 ⁿ -t, where n and t are determined to be different values.

As described above, since the first integer and the second integer are assumed to be integers smaller than a decimal number, the bits of the first binary number and the second binary number converted by the first transform unit 10 and the second transform unit 20 are converted. Has a value of n bits because one bit is smaller than the bit corresponding to the number of bits (n + 1).

The first adder 40 adds a binary number, which has been complemented to a second binary number, a first binary number and 1, and the second adder 50 adds a reference integer determined corresponding to the second binary number and a decimal point. The third adder 60 adds the binary number, the first binary number, and 1, which have been complemented, to the sum result of the second adder 50.

At this time, the complementary processing means to invert 0 or 1 of each bit of binary number represented by n bits.

Since the process of calculating the remainder when a number is divided depends on whether the dividend is a positive or negative number, the case is divided into a positive integer and a negative integer.

First, in the case where the first integer is greater than or equal to the second integer, that is, the dividend is a positive integer, the following relationship is established.

Equation 2

Therefore, the remainder obtained by dividing " ²ⁿ + 1st integer-2nd integer" as a dividend by a decimal number and removing ²ⁿ after the operation can obtain the same result.

At this time, in this embodiment, since the remainder is calculated in binary form, removing 2 ⁿ means ignoring the (n + 1) th bit and using a value from the first bit to the n th bit.

The above-described "2 ⁿ + first integer-second integer" can be expressed by Equation 3 below.

Equation 3

At this time, "~ 2nd integer" means processing the 2nd binary number which converted the 2nd integer.

As shown in Equation 3, when the first integer is greater than or equal to the second integer, the remainder obtained by subtracting the result of subtraction of the first integer and the second integer by a decimal number is the sum of the complementary binary number, the first binary number, and the first one. You can see that it is calculated in the form of.

Therefore, in the present exemplary embodiment, the first adder 40 adds the binary number, the first binary number, and 1, which are complemented to the second binary number, and transfers the first binary number to the controller 70, which will be described later. In the case of more than the second integer, the sum result of the first adder 40 may be determined as the remainder obtained by dividing the subtraction result of the first integer and the second integer by a decimal number.

Next, when the first integer is less than the second integer, that is, the dividend is a negative integer, the remainder obtained by dividing the difference between the first integer and the second integer by a decimal number becomes "fraction + first integer-second integer".

If this is changed, it can be expressed as Equation 4 below.

Equation 4

That is, when the first integer is less than the second integer, the result of subtracting the first integer and the second integer divided by a decimal number is the sum of the complementary binary number, the first binary number, and 1 You can see that it is calculated in the form of.

Therefore, in the present embodiment, the second adder 50 first adds t determined in correspondence with the second binary number and the decimal, and the third adder 60 compensates for the addition result of the second adder 50. The processed binary number, the first binary number, and 1 are added to the control unit 70, and the control unit 70 transmits the sum result of the third adder 60 to the first integer when the first integer is less than the second integer. The subtraction result of the second integer can be determined as the remainder divided by the decimal.

As described above, in the present embodiment, since the result of subtraction of the first integer and the second integer is calculated through separate adders 40 to 60 positioned in parallel, the first integer and the second integer are calculated. If only the magnitude relationship of integers is known, the sum result may be determined to be the remainder obtained by subtracting the first and second integer subtraction results by a decimal.

As described above, when the first integer is equal to or greater than the second integer, since 2 ⁿ is added, the sum of the first adder 40 indicates that the (n + 1) th bit is 1.

Therefore, in the present exemplary embodiment, the controller 70 determines that the first integer is greater than or equal to the second integer when the (n + 1) th bit included in the sum of the first adder 40 is 1, and (n + 1) If the first bit is 0, it may be determined that the first integer is less than the second integer.

That is, in the present exemplary embodiment, since the bits included in the sum result of the first adder 40 are simply checked without any complicated calculation process, the magnitudes of the first and second integers may be easily determined. The remainder of the result of subtracting an integer and a second integer divided by a decimal number can be calculated.

If it is determined that the first integer is greater than or equal to the second integer, the n-bit binary number included in the sum result of the first adder 40 may be determined as the remainder obtained by dividing the subtraction result of the first and second integers by a fraction. have.

On the other hand, if it is determined that the first integer is less than the second integer, n-bit binary numbers included in the summation result of the third adder 60 may be determined as the remainder obtained by dividing the subtraction result of the first integer and the second integer by a fraction. .

In the present embodiment, a plurality of

complementary processing units

90 and 100 for performing the above-described complementary processing of the binary number and the complementary processing of the sum result of the second adder 50 may be included.

Specifically, the first repair processing unit 90 repairs the second binary number, and the second repair processing unit 100 repairs the sum result of the second adder 50.

In particular, the first repair processing unit 90 and the second repair processing unit 100 according to the present embodiment may be configured as an inverter as shown in FIG. 1, but is not limited thereto. It may include any configuration.

In addition, the present embodiment may further include a third conversion unit 30 for converting a binary number to a decimal number, and an output unit 80 for outputting an operation result.

That is, the third converter 30 converts the remainder obtained by subtracting the subtraction result of the first integer and the second integer determined by the controller 70 into decimal numbers to be intuitively recognized by the user, and outputs the output unit 80. Outputs a decimal number converted by the third conversion unit 30.

Looking at the implementation process of the method for calculating the remainder according to an embodiment of the present invention with reference to Figure 2, first, the first transform unit 10 and the second transform unit 20 inputs the first integer and the second integer The first binary number and the second binary number are respectively converted into n bits (S10).

In addition, the first adder 40 adds the first binary number and the first binary number to which the second binary number is repaired through the first complement processing unit 90 (S20).

Subsequently, the second adder 50 adds the second binary number and the predetermined reference constant t (S30), and the third adder 60 passes through the second maintenance processor 100 to add the second adder 50. In step S40, the binary number, the first binary number, and 1, which are complemented with the summation result, are added.

Next, the controller 70 determines the remainder obtained by dividing the subtraction result of the first integer and the second integer by a decimal number based on the magnitude of the first integer and the second integer (S50).

As described above, in the present embodiment, since the result of subtracting the result of subtraction of the first integer and the second integer is divided by a decimal number, the operation is performed through separate adders 40 to 60, which are placed in parallel (S20 to S40). If only the magnitude relationship between the first integer and the second integer is known, the corresponding summation result can be determined to be the remainder of the subtraction of the first and second integers divided by the decimal.

Specifically, if the first integer is greater than or equal to the second integer, the control unit 70 divides the n-bit binary number included in the sum result of the first adder 40 by dividing the result of subtracting the first integer from the second integer by a decimal number. Determine (S60).

On the other hand, if the first integer is less than the second integer, the control unit 70 divides the n-bit binary number included in the sum result of the third adder 60 by dividing the subtraction result of the first integer and the second integer by a fraction. Determine (S62).

As described above, in the present embodiment, a simple operation is performed in a different manner according to the magnitude relationship between the first integer and the second integer, and any operation result is reflected by the magnitude relationship between the first integer and the second integer. Determines whether two integer subtraction results are divided by decimals.

Subsequently, the third conversion unit 30 converts the binary number determined by dividing the subtraction result of the first integer and the second integer into decimals (S70), and the output unit 80 outputs the converted decimal number to the user. Lets simply check the remainder of the difference between the first integer and the second integer divided by a decimal number.

According to the present exemplary embodiment, the remainder obtained by subtracting the result of subtraction of two integers through a plurality of adders regardless of the magnitude relationship of two integers, and later subtracting the result of subtraction of two integers by a decimal number according to the magnitude relationship of two integers By determining the remainder, we can compute the remainder faster.

In addition, the present embodiment can simply determine the magnitude relationship of two integers by checking the most significant bit included in the sum result.

Although the present invention has been described with reference to the embodiments shown in the drawings, it is merely exemplary and various modifications and equivalent other embodiments are possible to those skilled in the art. I will understand. Therefore, the true technical protection scope of the present invention will be defined by the claims below.

Claims

In the device for calculating the remainder of the result of subtracting two integers divided by the prime number,

A first converting unit and a second converting unit which receive the first integer and the second integer and convert the first integer and the second binary into n bits, respectively;

A first adder configured to add the first binary number and the first binary number to which the second binary number is complemented;

A second adder configured to add the second binary number and a reference integer determined corresponding to the decimal number;

A third adder configured to add the first binary number and the first binary number to which the complementary result of the sum of the second adder is processed; And

Based on the magnitude of the first integer and the second integer, one of the sum result of the first adder or the sum result of the third adder is selected, and if the first integer is greater than or equal to the second integer, the first adder Control unit for determining the n-bit binary number included in the sum result as the remainder of the result of subtraction of the first integer and the second integer divided by a decimal number

Apparatus for calculating the remainder comprising a.
The method of claim 1,

And a second maintenance processor configured to perform a complement processing of the sum result of the first complement processing unit and the second adder to perform the complement processing on the second binary number.
The method of claim 1,

And the reference constant is set to t when the decimal number is represented by 2 n -t.
The method of claim 1,

The control unit determines that, when the first integer is less than the second integer, the n-bit binary number included in the sum result of the third addition unit is determined by dividing the difference between the first integer and the second integer by a decimal number. Device that calculates the remainder.
The method of claim 1,

The controller determines that the first integer is greater than or equal to the second integer when the (n + 1) th bit included in the sum of the first adder is 1, and the (n + 1) th bit included in the sum result. Is 0, the first integer is determined to be less than the second integer.
The method of claim 1,

A third converter converting the binary number determined by the control unit to the remainder by dividing the difference between the first integer and the second integer by a decimal number; And

An output unit for outputting a decimal number converted by the third conversion unit

Apparatus for calculating the remainder further comprises.
In the method of calculating the remainder of the result of subtracting two integers divided by a prime number,

A first converting unit and a second converting unit receiving the first integer and the second integer and converting the first binary number and the second binary number to n bits, respectively;

Adding a first binary addition and a complementary binary number by the first addition unit to the first binary number and 1;

Summing a second integer and a reference integer determined in correspondence with the decimal part;

Adding a third binary addition-complementary binary number, the first binary number and the first one, of which the complementary result of the second addition unit is added; And

And determining, by the controller, a result of dividing the subtraction result of the first integer and the second integer by a decimal number based on the magnitude of the first integer and the second integer, wherein the controller is configured to determine the first integer as the second integer. And if it is an integer or more, determine the n-bit binary number included in the sum result of the first adder as the remainder obtained by dividing the subtraction result of the first and second integers by a fraction.
The method of claim 7, wherein

In the determining of a result of dividing the subtraction result of the first integer and the second integer by a fraction, the control unit, when the first integer is less than the second integer, n-bit binary number included in the sum result of the third adder And subtracting the result of the subtraction of the first integer and the second integer into a remainder divided by a decimal number.
The method of claim 7, wherein

In the step of summing the second binary number and the reference constant determined corresponding to the decimal, wherein the reference constant is set to t when the decimal is represented by 2 n -t.
The method of claim 7, wherein

In the determining of the remainder obtained by dividing the subtraction result of the first integer and the second integer by a decimal number, the controller determines that the first integer is equal to (n + 1) th bit included in the sum result of the first adder; And determining that the second integer is equal to or greater than the second integer, and determining that the first integer is less than the second integer when the (n + 1) th bit included in the sum result is 0.
The method of claim 1,

After determining the remainder by dividing the subtraction result of the first integer and the second integer by a decimal number, the third conversion unit converts the binary number determined by dividing the subtraction result of the first integer and the second integer by a decimal number to a decimal number. step; And

Outputting the converted decimal number by the output unit

Method for calculating the remainder further comprises.