Patent Publication Number: US-8996599-B2

Title: Arithmetic device for calculating between physical quantities including units, and database used thereby

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2011-209988, filed on Sep. 26, 2011, the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein generally relate to an arithmetic device and a database. 
     BACKGROUND 
     Generally, for a calculation between different physical quantities including units, the calculation is performed based on string processing. 
     However, for a calculation between different physical quantities including units and prefixes, if the calculation is performed based on the string processing, the handling may be very complicated because the differences in order of arithmetic expressions and in notation (font and the like) of units and prefixes should be taken into consideration for the string processing. 
     Moreover, it is difficult to accurately collate the units resulting from the calculation and thus it is difficult to obtain the calculation result without an error. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating a configuration of an arithmetic device according to a first embodiment. 
         FIG. 2  is a flowchart illustrating a process by an assignment section of the arithmetic device according to the first embodiment (assignment to a base unit). 
         FIG. 3  is a flowchart illustrating another process by the assignment section of the arithmetic device according to the first embodiment (assignment to a derived unit). 
         FIG. 4  is a flowchart illustrating a process by an arithmetic section of the arithmetic device according to the first embodiment. 
         FIG. 5  is a diagram illustrating a configuration of an arithmetic device according to a second embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     In view of the above circumstances, an aspect of embodiments provides an arithmetic device including: a database that stores a first indicator representing a base unit included in a unit system being assigned with a prime number other than a prime factor of a prefix which is expressed with a base, including the prime factor, and an exponential part, and a second indicator representing a derived unit expressed by combining the base units in a form of a simple fraction including a numerator and a denominator each of which is assigned with an integer which is the product of the first indicators; a conversion section that obtains a plurality of physical quantities each including a quantity, a prefix, and a unit, when the unit belongs to the base unit, the conversion section obtaining a third indicator by converting the unit into the first indicator and multiplying the converted first indicator by the prefix, or when the unit belongs to the derived unit, the conversion section obtaining the third indicator by converting the unit into the second indicator and multiplying the converted second indicator by the prefix; and an arithmetic section that performs a calculation between the quantities of the plurality of physical quantities and between the third indicators. 
     In view of the above circumstances, another aspect of the embodiments provides a database that stores a first indicator representing a base unit included in a unit system being assigned with a prime number other than a prime factor of a prefix which is expressed with a base, including the prime factor, and an exponential part, and a second indicator representing a derived unit expressed by combining the base units in a form of a simple fraction including a numerator and a denominator each of which is assigned with an integer which is the product of the first indicators. 
     According to the aspects of embodiments, a calculation can be performed between different physical quantities including a unit and a prefix without an error. 
     Herein below, embodiments for carrying out the invention will be described. 
     First Embodiment 
       FIG. 1  is a diagram illustrating a configuration of an arithmetic device  1000  according to a first embodiment. 
     The arithmetic device  1000  according to this embodiment performs a calculation between different physical quantities each including a prefix and a unit. 
     The arithmetic device  1000  illustrated in  FIG. 1  includes an assignment section  10 , a conversion section  20 , an arithmetic section  30 , a database  50 , a storage section  60 , an input device  70  such as a keyboard, and an output device  80  such as a display. Further, the assignment section  10 , the conversion section  20 , and the arithmetic section  30  are implemented by an arithmetic processing device  100  such as a CPU or the like. In addition, the database  50  and the storage section  60  are implemented by a storage device  200  such as a memory. 
     Herein below, the functions of the assignment section  10  will be described in detail. 
     The assignment section  10  assigns a unique prime number (hereinafter, referred to as a first indicator), as an identifier (ID) to be uniquely determined, to each of the SI base units for physical quantities, and stores the identifiers into the database  50 . 
     In addition, the assignment section  10  assigns a set of unique integers (hereinafter, referred to as a second indicator) to a derived unit which is obtained by combining the SI base units and can be expressed in the form of a simple fraction when combined, and stores the set as an integer value into the database  50 . 
     (Base Unit) 
       FIG. 2  is a flowchart illustrating a process of assigning the first indicator to a base unit. 
     The assignment section  10  counts up integers in ascending order (S 101 ), and determines whether or not the counted integer is a prime number based on a known method, for example, the Erastothenes&#39; sieve, the Adleman-Pomerance-Rumely (APR) primality test, or the like (S 102 ). 
     Here, the prime numbers under 100 include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 
     In a case where the counted integer is a prime number, the assignment section  10  refers to a first list which includes base units to be assigned with first indicators stored in the storage section  60 . Then, the assignment section  10  extracts base units one by one in order of the first list (S 103 ). The assignment section  10  assigns one of the first indicators to the extracted base unit (S 104 ). In a case where the counted integer is not a prime number, the assignment section  10  resumes counting up integers until a prime number appears. 
     The assignment section  10  assigns a unique first indicator to each of the base units (including dimensionless quantities) which have been listed in the first list stored in the storage section  60  (S 105 ). 
     Table 1 is a table illustrating an example of the first indicator assigned to the SI base units (m, Kg, s, A, K, Cd, and mol). 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                 SI  
                 First  
               
               
                   
                 Base unit 
                 unit 
                 indicator 
               
               
                   
                   
               
             
            
               
                   
                 Length 
                 m 
                  3 
               
               
                   
                 Mass 
                 Kg 
                  7 
               
               
                   
                 Time 
                 s 
                 11 
               
               
                   
                 Electric current 
                 A 
                 13 
               
               
                   
                 Temperature 
                 K 
                 17 
               
               
                   
                 Luminous intensity 
                 Cd 
                 19 
               
               
                   
                 Amount of substance 
                 mol 
                 23 
               
               
                   
                   
               
            
           
         
       
     
     Further, the dimensionless quantities such as radian, steradian, and the like are set to 1 (dimension=1) in the SI units, which is different from integers corresponding to the physical quantities. Therefore, each dimensionless quantity can be assigned with a unique first indicator so as to be treated as a base unit. 
     As listed in Table 2, regarding the dimensionless quantities (rad, sr, etc.) as the base units, the assignment section  10  can assign the unique first indicators to the dimensionless quantities. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Dimensionless  
                 SI 
                 First  
               
               
                   
                 quantity 
                 unit 
                 indicator 
               
               
                   
                   
               
             
            
               
                   
                 Radian 
                 rad 
                 29 
               
               
                   
                 Steradian 
                 sr 
                 31 
               
               
                   
                   
               
            
           
         
       
     
     (Derived Unit) 
     A derived unit in the SI units can be expressed by combining the base units, that is, by performing multiplication or division between the base units (for example, Newton N=kg·m/s 2 ). As listed in Table 3, the relation between the derived units and the base units can be stored in advance in the storage section  60  as a second list. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                   
                   
                   
                 Expression  
               
               
                   
                   
                 Name  
                 SI  
                 in terms of  
               
               
                   
                 Derived unit 
                 of unit  
                 unit 
                 SI base unit 
               
               
                   
                   
               
             
            
               
                   
                 Frequency 
                 Hertz 
                 Hz 
                 s −1   
               
               
                   
                 Force 
                 Newton 
                 N 
                 m · kg · s −2   
               
               
                   
                 Pressure/Stress 
                 Pascal 
                 Pa 
                 m −1  · kg · s −2   
               
               
                   
                 Energy/Work 
                 Joule 
                 J 
                 m 2  · kg · s −2   
               
               
                   
                 Power 
                 Watt 
                 W 
                 m 2  · kg · s −3   
               
               
                   
                 Electric 
                 Coulomb 
                 C 
                 s · A 
               
               
                   
                 charge/Quantity  
                   
                   
                   
               
               
                   
                 of electricity 
                   
                   
                   
               
               
                   
                 Voltage/  
                 Volt 
                 V 
                 m 2  · kg · s −3  · A −1   
               
               
                   
                 Electrical 
                   
                   
                   
               
               
                   
                 potential 
                   
                   
                   
               
               
                   
                 difference 
                   
                   
                   
               
               
                   
                 Electric 
                 Farad 
                 F 
                 m −2  · kg −1  · s 4  · A 2   
               
               
                   
                 capacitance 
                   
                   
                   
               
               
                   
                 Electric 
                 Ohm 
                 Ω 
                 m 2  · kg · s −3  · A −2   
               
               
                   
                 resistance 
                   
                   
                   
               
               
                   
                 Conductance 
                 Siemens 
                 S 
                 m −2  · kg −1  · s 3  · A 2   
               
               
                   
                 Magnetic flux 
                 Weber 
                 Wb 
                 m 2  · kg · s −2  · A −1   
               
               
                   
                 Magnetic flux  
                 Tesla 
                 T 
                 kg · s −2  · A −1   
               
               
                   
                 density 
                   
                   
                   
               
               
                   
                 Inductance 
                 Henry 
                 H 
                 m 2  · kg · s −2  · A −2   
               
               
                   
                 Luminance 
                 Lux 
                 1x 
                 m −2  · cd 
               
               
                   
                 Radioactivity 
                 Becquerel 
                 Bq 
                 s −1   
               
               
                   
                 Absorbed dose 
                 Gray 
                 Gy 
                 m 2  · s −2   
               
               
                   
                 Equivalent dose 
                 Sievert 
                 Sv 
                 m 2  · s −2   
               
               
                   
                 Catalytic activity 
                 Katal 
                 kat 
                 s −1  · mol 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 3  is a flowchart illustrating a process of assigning the second indicator to the derived unit. 
     The assignment section  10  reads out the prime numbers assigned to the base units as the first indicators from the database  50 . The assignment section  10  extracts a derived unit in order of the second list with reference to the second list stored in the storage section  60  (S 201 ). Then, for each of the numerator and the denominator, the assignment section  10  multiplies the prime numbers, which are the first indicators representing the base units that constitute the numerator or the denominator, in accordance with the expression in which the base units of the derived unit are used (S 202 ). For example, in regard to the expression of Newton (N) in which base units are used, the numerator is expressed as Kg·m. Therefore, based on the first indicators of the base units listed in Table 1, ‘7×3=21’ is obtained. Similarly, since the denominator is s 2 , ‘11×11=121’ is similarly obtained based on Table 1. 
     The assignment section  10  assigns a sequence, which is an integer set of the numerator and the denominator, to the derived unit as the second indicator (S 203 ), and stores the sequence in the database  50 . According to the example of Newton (N) described above, the second indicator for Newton (N) is given (21, 121). 
     The assignment section  10  assigns a unique second indicator to each of the derived units listed in the second list which is stored in the storage section  60  (S 204 ). 
     Table 4 is a table showing an example in which the second indicators are assigned to the derived units in the SI units. Further, in a case where any one of the numerator and the denominator is dimensionless like the derived units such as Frequency (Hz) and Coulomb (C) listed in Table 4, the dimensionless unit is set to 1, and then a set of “1” and an integer is assigned as the second indicator. In other words, in the example of Table 4, (1, 11) is assigned for Frequency (Hz) and (143, 1) is assigned for Coulomb (C). 
     In addition, for example, in a case where a plurality of the derived units are in the same dimension like the derived units such as Frequency (Hz), Radioactivity (Bq), and the like, the numerator or the denominator is multiplied by a unique prime number for identifying the unit so that different second indicators are assigned to respective derived units. In the example of Frequency (Hz) and Radioactivity (Bq) listed in Table 4, since both derived units are expressed with s −1 , (1, 11) is assigned to Frequency (Hz) as the second indicator. For distinguishing Radioactivity (Bq) from Frequency (Hz), the prime number 37 is multiplied by the numerator, thereby assigning (37, 11) as the second indicator. 
     Similarly, for example, the absorbed dose shown with Gray (Gr) and the equivalent dose shown with Sievert (Sv) are in the same dimension of [m 2 ·s −2 ] Further, the equivalent dose is a value calculated by multiplying the absorbed dose by an effective count (W R ) regarding a human body which is different depending on the type of radiation. Therefore, by assigning one prime number of 41 to the effective count (W R ), in a case where the absorbed dose is expressed as (9, 121), the equivalent dose can be expressed as (9×41, 121)=(369, 121). With the second indicator determined as above, the absorbed dose and the equivalent dose can be distinguished from each other. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                   
                   
                   
                 Expression 
                   
               
               
                   
                   
                   
                 in terms  
                   
               
               
                   
                 Named 
                 SI  
                 of SI  
                 Second 
               
               
                 Derived unit 
                 unit 
                 unit 
                 base unit 
                 indicator 
               
               
                   
               
             
            
               
                 Frequency 
                 Hertz 
                 Hz 
                 s −1   
                 (1, 11) 
               
               
                 Force 
                 Newton 
                 N 
                 m · kg · s −2   
                 (21, 121) 
               
               
                 Pressure/Stress 
                 Pascal 
                 Pa 
                 m −1  · kg · s −2   
                 (7, 363) 
               
               
                 Energy/Work 
                 Joule 
                 J 
                 m 2  · kg · s −2   
                 (63, 121) 
               
               
                 Power 
                 Watt 
                 W 
                 m 2  · kg · s −3   
                 (63, 1331) 
               
               
                 Electric 
                 Coulomb 
                 C 
                 s · A 
                 (143, 1) 
               
               
                 charge/Quantity  
                   
                   
                   
                   
               
               
                 of electricity 
                   
                   
                   
                   
               
               
                 Voltage/ 
                 Volt 
                 V 
                 m 2  · kg · s −3  · A −1   
                 (63,  
               
               
                 Electrical 
                   
                   
                   
                 17303) 
               
               
                 potential 
                   
                   
                   
                   
               
               
                 difference 
                   
                   
                   
                   
               
               
                 Electric 
                 Farad 
                 F 
                 m −2  · kg −1  · s 4  · A 2    
                 (2474329, 
               
               
                 capacitance 
                   
                   
                   
                 63) 
               
               
                 Electric 
                 Ohm 
                 Ω 
                 m 2  · kg · s −3  · A −2   
                 (63, 
               
               
                 resistance 
                   
                   
                   
                 224939) 
               
               
                 Conductance 
                 Siemens 
                 S 
                 m −2  · kg −1  · s 3  · A 2    
                 (224939, 
               
               
                   
                   
                   
                   
                 63) 
               
               
                 Magnetic flux 
                 Weber 
                 Wb 
                 m 2  · kg · s −2  · A −1   
                 (63, 1573) 
               
               
                 Magnetic flux 
                 Tesla 
                 T 
                 kg · s −2  · A −1   
                 (7, 1573) 
               
               
                 density 
                   
                   
                   
                   
               
               
                 Inductance 
                 Henry 
                 H 
                 m 2  · kg · s −2  · A −2   
                 (63, 
               
               
                   
                   
                   
                   
                 20449) 
               
               
                 Luminance 
                 Lux 
                 1x 
                 m −2  · cd 
                 (19, 121) 
               
               
                 Radioactivity 
                 Becquerel 
                 Bq 
                 s −1   
                 (37, 11) 
               
               
                 Absorbed dose 
                 Gray 
                 Gy 
                 m 2  · s −2   
                 (9, 121) 
               
               
                 Equivalent dose 
                 Sievert 
                 Sv 
                 m 2  · s −2   
                 (369, 121) 
               
               
                 Catalytic activity 
                 Katal 
                 kat 
                 s −1  · mol 
                 (23, 11) 
               
               
                   
               
            
           
         
       
     
     Herein below, the functions of the conversion section  20  and the arithmetic section  30  will be described in detail. 
     After the assignment section  10  stores the first and second indicators in the database  50  for all of the base units listed in the first list and the derived units listed in the second list, the arithmetic device  1000  performs a calculation between the different physical quantities using the first and second indicators stored in the database  50 . 
     For example, when a user has inputted a physical quantity in the form of a string of a quantity and a string of a unit using the input device  70  at the time of designing, the conversion section  20  converts the string of a unit, input by the user, into a corresponding second indicator with reference to the database  50 . Then, a set of the quantity and the second indicator is stored as a sequence in the storage section  60 . 
     For example, when a user inputs a string of “50 N” using the input device  70 , the conversion section  20  converts the string of Newton (N) into (21, 121) that is the second indicator with reference to the database  50 . 
     Then, as a sequence which is a combination of the quantity “50” and the second indicator “(21, 121)”, the sequence “(50, 21, 121)” is stored in the storage section  60 . Further, in a case of the base unit, the denominator of the second indicator is set to an integer of 1. 
     Further, the user can input a prefix (k, M, G, etc.) in addition to the unit using the input device  70 . In general, the prefix can be expressed in the form of Z n , where Z represents a base and n represents an exponential part. Further, as the base Z, “10” is used for typical physical quantities, or 1024 (=2 10 ) is used for volume of information such as a bit or a byte. The relation between the prefix and Z n  can be stored in the database  50  in advance as a third list. 
     When the user inputs a prefix in the form of a string using the input device  70 , the conversion section  20  converts the string into the exponential part of Z n , that is, into n that represents the prefix, by referring to the third list. Then, the conversion section  20  stores a set of the quantity, the second indicator, and the exponential part in the storage section  60  as a sequence. 
     For example, when the user inputs “50 kN” (50, N, and k represent a quantity, a unit, and a prefix, respectively) using the input device  70 , the conversion section  20  converts Newton (N) into (21, 121) that is a second indicator with reference to the database  50 . In addition, the conversion section  20  converts k into 3 which is the exponential part of 10 3 . Then, the conversion section  20  stores the sequence (50, 21, 121, 3) which is a set of the quantity of 50, the second indicator, and the exponential part, in the storage section  60 . 
     In addition, the user may input an arithmetic expression including different physical quantities using the input device  70 . In this case, the conversion section  20  converts each of the physical quantities into a sequence. However, for convenience of calculation to be described later, the conversion section  20  converts the physical quantity right after the division symbol “÷” or “/” into a sequence including a reciprocal number of the quantity, a second indicator in which the denominator and the numerator are exchanged in their positions, and a negative value of the exponential part. 
     When the user inputs an arithmetic expression of a plurality of different physical quantities in the form of a string, the arithmetic section  30  performs a calculation between the different physical quantities using the sequence (hereinafter, referred to as the sequence (a, b, c, d)) of the quantity, the second indicator, and the exponential part, which are converted by the conversion section  20  and stored in the storage section  60 . 
     In the calculation performed between the plurality of different physical quantities, there is a feature as below depending on whether or not the units are equal to each other (a case of the arithmetic expression represented in the form of multiplication). Further, in this case, a suffix (1, 2, . . . , n) is added in correspondence with the different physical quantity. 
     (i) In the case of different unit 
                     (       α   1     ×     α   2     ×   …   ×     α   n       )     ×     (         b   1     ×     b   2     ×   …   ×     b   n           c   1     ×     c   2     ×   …   ×     c   n         )     ×     B       d   1     +     d   2     +   …   +     d   n                 (     Equation   ⁢           ⁢   1     )               
(ii) In the case of the same unit (b=b 1 =b 2 = . . . =b n , c=c 1 =c 2 = . . . =c n , d=d 1 =d 2 = . . . d n )
 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         α 
                         1 
                         ′ 
                       
                       + 
                       
                         α 
                         2 
                         ′ 
                       
                       + 
                       … 
                       + 
                       
                         α 
                         n 
                         ′ 
                       
                     
                     ) 
                   
                   × 
                   
                     b 
                     c 
                   
                   × 
                   
                     B 
                     d 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
       FIG. 4  is a flowchart illustrating a process of calculation performed by the arithmetic section  30 . 
     Specifically, the arithmetic section  30  obtains the sequence (a, b, c, d) for a plurality of physical quantities which have been converted by the conversion section  20  and stored in the storage section  60  (S 301 ). At this time, the arithmetic section  30  sets d to 0 for the physical quantity to which the prefix has not been input so as to obtain a sequence (a, b, c, 0). 
     The arithmetic section  30  refers to all of the sequences obtained from the storage section  60  (S 302 ). In a case where any one of b and c in the second indicator in each of the sequences is different from each other (that is, the case where the units are different from each other), the arithmetic section  30  performs a multiplication (πa=A) with the quantities based on Equation 1 (S 303 ). In addition, the arithmetic section  30  performs a multiplication (πb=B′) with the numerators in the second indicators, a multiplication (πc=C′) with the denominators in the second indicators (S 304  and S 305 ). Then, the arithmetic section  30  performs a division (reduction) with B′ and C′ and a common factor, thereby calculating B and C (S 306 ). In addition, the arithmetic section  30  performs an addition (Σd=D) with the exponential parts (S 307 ). 
     The arithmetic section  30  obtains a sequence (A, B, C, D) representing the physical quantity resulting from the calculations described above (S 308 ), and stores the sequence in the storage section  60 . 
     (Specific Example of Calculation) 
     Herein below, a specific calculation will be described based on an example of calculating Pressure (Pa). 
     A unit of Pressure (Pa) can be obtained by dividing Newton (N) by Area (m 2 ). For example, when a person weighing 50 kg gets on a stage of 50 cm 2  under the acceleration of gravity of 1 G (9.8 m/s 2 ), pressure applying on the stage can be calculated by 50 kg×9.8 m/s 2 ÷50 cm 2 . 
     Herein, when the user inputs a string of “50 kg×9.8 m/s 2 ÷50 cm 2 ” using the input device  70  to calculate pressure, the conversion section  20  converts “50 kg” into a sequence of (50, 7, 1, 0), “9.8 cm 2 ” into a sequence of (9.8, 3, 11 2 , 0), and “50 cm 2 ” into a sequence of (50 −1 , 1, 3 2 , −(−2)×2), and stores the sequences in the storage section  60 . 
     The arithmetic section  30  performs a multiplication “50×9.8×(50 −1 )” of the quantities, multiplications “7×3×1” and “1×11 2 ×3 2 ” of the second indicators, and an addition “0+0+(2×2)” of the exponential parts with reference to each of the sequences from the storage section  60  according to the flowchart illustrated in  FIG. 4 . Further, the arithmetic section  30  performs a reduction on the units, thereby obtaining the sequence (9.8, 7, 363, 4) representing the calculated physical quantities. Then, the arithmetic section  30  stores the obtained sequence in the storage section  60 . 
     Further, in a case where the arithmetic expression includes the addition and subtraction operations, the arithmetic section  30  can perform calculations according to Equation 2. In this case, for example, it is determined that the units are equal to each other, so that the arithmetic section  30  performs a calculation when the units are the same. In a case where it is determined that the units are not the same, an error message is displayed by the output device  80  which will be described later, through which the user can visually recognize the result. 
     In addition, in a case where the arithmetic expression includes a combination of four arithmetic operations, the arithmetic section  30  may perform calculations according to Equations 1 and 2. 
     The conversion section  20  converts the unit into a string of the derived unit or the base unit where the second indicator is matched with the portion (B, C) representing the unit of the sequence (A, B, C, D) which is stored in the storage section  60  by the arithmetic section  30 , with reference to the second indicator of the derived unit stored in the database  50 . 
     In addition, the conversion section  20  converts the exponential part into the prefix with reference to the third list stored in the database  50 . At this time, if necessary, a multiplier factor in a floating point expression is adjusted, and the adjusted multiplier factor is added to the exponential part, and then the resultant exponential part is converted into the string of the prefix. 
     The output device  80  displays the conversion result of the conversion section  20  in a form of a string enumerated in order of the quantity, the prefix, and the unit. Then, the output device  80  outputs the calculation result so that the user can visually recognize the calculation result. 
     With the arithmetic device  1000  according to this embodiment, by using the first and the second indicators assigned to the unit, even when calculation is performed between the different units, an error in the result caused by performing an unexpected reduction in the calculation between the prime numbers can be prevented. In addition, the unit can be identified regardless of an expression style (order etc.) of the derived unit. 
     In addition, the physical quantity is expressed in a simple sequence set of integers such as “the quantity, the unit, the exponential part of the prefix”. Further, calculation is divided into three parts in which the same kind of integers are calculated just like quantity from quantity, unit from unit, and exponential part from exponential part. Therefore, calculation between different physical quantities including the unit and the prefix can be performed simply. 
     Further, according to this embodiment, the description has been made in connection with an example in which a user input a string such as an arithmetic expression using the input device  70  at the time of designing. In a case where a control target apparatus connected to the arithmetic device  1000  is necessary to be controlled or a physical quantity is required for diagnosing the apparatus, an arithmetic expression can be automatically obtained. In addition, instead of the arithmetic expression, a physical quantity such as a maximum allowable voltage may be assigned as an indicator to a device such as a cable connected to the arithmetic device  1000  (direct notation, or notation by putting an information tag on an electronic medium such as an RFID and an optical medium such as a bar code). Therefore, the arithmetic device  1000  can be used as a management system so that the operation of the devices is managed in a normal state. 
     In addition, according to this embodiment, the description has been made in connection with an example of only the SI units. However, the invention is not limited the example, but can be applied to the imperial units or the like other than the SI units. 
     In this case, for example, a physical indicator representing “quantity”, the kind (concept) of physical quantity such as the unit notation, the length, the weight, or the like, which expresses the units (the SI units, the imperial units, etc.), is added in the sequence. For example, Meter (m) in the SI units and Yard (yd) in the imperial units belong to the same “quantity” as length. 
     Then, a conversion expression for converting the unit is stored as a list in the database  50 . Therefore, in a case where the unit indicators are different but the physical indicators are equal, the arithmetic section  30  can convert the physical quantities between the different units with reference to the conversion expression. 
     (Modification) 
     In the first embodiment, in order to express the prefix, the exponential part of the prefix is assigned as an integer in the sequence in addition to the unit. In this modification, the unit and the prefix will be expressed at the same time. 
     The assignment section  10  assigns prime numbers other than 2 and 5 among the prime numbers as the first indicators in the base unit. In addition, the assignment section  10  assigns the first indicators of the base unit to the derived unit. Further, the assignment performed in this modification is the same as that in the first embodiment except the above point, so that the detailed description will be not repeated herein. 
     Similarly to the first embodiment, when a user inputs a string of the quantity of the physical quantity, the prefix, and the unit using the input device  70 , the conversion section  20  converts the string of the unit input by the user into the second indicator with reference to the database  50 . 
     In addition, the conversion section  20  converts the string into Z n  representing the prefix with reference to the third list. In a case where n is positive, Z n  is multiplied by an integer representing the numerator in the second indicator of the unit. In a case where n is negative, Z −n  is multiplied by an integer representing the denominator. Then, the resultant value is stored in the storage section  60  as a sequence of the quantity and a third indicator of the unit on which the prefix are reflected. 
     For example, when the user inputs “50 kN” (50 as the quantity, N as the unit, and k as the prefix) using the input device  70 , the conversion section  20  converts Newton (N) into (21, 121) as the second indicator with reference to the database  50 . In addition, the conversion section  20  converts k into 10 3 =1000 with reference to the storage section  60 , and multiplies  21  representing the numerator of the second indicators by 1000 to obtain 21000. Then, the conversion section  20  stores, in the storage section  60 , the sequence set (50, 21000, 121) of the quantity of 50 and the third indicator on which the prefix is reflected. 
     When the user inputs a plurality of different physical quantities in a form of a string, the arithmetic section  30  performs calculation between the different physical quantities using the sequence (hereinafter, denoted by the sequence (a, e, f)) of the quantity and the third indicator on which the prefix is reflected, which are converted by the conversion section  20  and stored in the storage section  60 . 
     In a case where the arithmetic section  30  determines that the units are different from each other with reference to all of the sequences obtained from the storage section  60 , the arithmetic section  30  performs multiplication between the quantities (πa=A). In addition, the arithmetic section  30  performs multiplication between the numerators in the third indicator (πe=E′), between the denominators in the third indicator (πf=F′), and performs division (reduction) on each multiplied result by a common factor of E′ and F′, so that E and F are calculated. 
     Then, the arithmetic section  30  stores, in the storage section  60 , a sequence (A, E, F) representing the physical quantities resulting from the calculations described above. 
     Therefore, the physical quantities becomes a set of integers including “the quantity, the unit including the prefix”, so that the expression of the sequence can be simplified further more. By separating the calculation of the quantities from that of the units including the prefix, the different physical quantities can be simply calculated further more. 
     Furthermore, since 2 and 5 are excluded from the first indicator of the base unit, when the units including the prefix are calculated, an unexpected reduction is not performed. Therefore, the calculation can be performed without an error. 
     In addition, the description has been made focusing on an example where a decimal system is employed, in which the base Z is set to 10 (in a case of the amount of information, 1024) as the exponential part representing the prefix. However, a single prime number or the product of plural prime numbers may be used as the base Z, for example. 
     In this case, the assignment section  10  assigns, to the base unit, a prime number as the first indicator excepting the prime number obtained by factorizing the base Z into prime factors. 
     As an example, in a case where the base Z is set to 21 as the prime number representing the prefix, the assignment section  10  factorizes  21  into 3 and 7, so that the prime numbers excepting 3 and 7 may be assigned to the base unit as the first indicator. In addition, in a case where the base Z is set to 7 as a single prime number, the assignment section  10  may assign the prime numbers excepting 7 to the base unit as the first indicator. 
     Therefore, similarly to the case where 2 and 5 as the prime factors of 10 are excluded when the base Z is expressed using the decimal system as described above, an unexpected reduction is not performed when the units including the prefix are calculated. Therefore, the calculation can be performed without an error. 
     The conversion section  20  separates the prefix Z n  from the integer of the third indicator, for example, using the prime factorization or the like. Then, the conversion section  20  converts the exponential part into the string of the prefix with reference to the third list stored in the database  50 . In addition, referring to the second indicator of the derived unit stored in the database  50 , the conversion section  20  converts the unit into a string of the derived unit or the base unit where the third indicator from which the prefix has been separated is matched with the second indicator. 
     Second Embodiment 
       FIG. 5  is a diagram illustrating a configuration of an arithmetic device  2000  according to a second embodiment. 
     The arithmetic device  2000  is different from the arithmetic device  1000  according to the first embodiment in that a checking section  40  is provided. Further, the same components as those of the arithmetic device  1000  will be denoted with the same reference numerals, and the description thereof will not be repeated. 
     The checking section  40  determines whether or not, when the arithmetic section  30  performs calculation between different physical quantities, the calculation result is a significant physical quantity. The checking section  40  is embodied using the arithmetic processing device  100  such as a CPU. 
     Herein below, the functions of the checking section  40  will be described in detail. 
     The unit obtained from the calculation result can be used for determining whether or not the physical quantity is significant. 
     For example, in a case where the unit obtained as a result of the multiplication or the division performed between the physical quantities is not found in a combination of the base units, it can be recognized that the calculation result is an insignificant physical quantity. On the contrary, in a case where the unit is found in a combination the base units, it can be recognized that the calculation result is a significant physical quantity. 
     The checking section  40  obtains the sequence (A, B, C, D) as the calculation result which is stored in the storage section  60  by the arithmetic section  30 , and extracts the unit portion (B, C) therefrom. Then, the checking section  40  checks the extracted unit (B, C) against the first or second indicator with reference to the first indicator of the base unit and the second indicator of the derived unit stored in the database  50 . 
     As a result, in a case where there is a unit which is matched with the unit (B, C), that is, both conditions B=b and C=c are satisfied in the first or second indicator stored in the database  50 , the checking section  40  determines that the calculation result is a significant physical quantity. 
     On the other hand, in a case where there is no unit which is matched with the extracted unit (B, C) in the first or second indicator stored in the database  50 , the checking section  40  determines that the calculation result is an insignificant physical quantity. In this case, for example, an error message may be displayed by the output device  80 , so that a user can be visually recognized. 
     With the arithmetic device  2000  according to this embodiment, only the calculation which obtains a significant physical quantity can be performed. Therefore, a human error caused by a user can be prevented in a user&#39;s designing process and the like. 
     With the arithmetic device according to at least one of the embodiments described above, calculation can be performed between different physical quantities including a unit and a prefix without an error. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel methods and systems described herein may be embodied in a variety of the other forms; furthermore, various omissions, substitutions and changes in the form the methods and systems described herein may be made without departing from the sprit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.