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Unit Codes

The unit codes are used in the DESCRIP0.UNITS, DESCRIP1.UNITS, DESCRIP2.UNITS, DESCRIP3.UNITS, and DESCRIP.UNITS record fields. It specifies the physical units for the data and its dimension. Each code is stored in an integer at least 32 bits long. The bits are numbered from 0 to 31, the least significant bit in the integer being number 0. Bits 29 to 31 define an index of eight possible forms of specifying units.

The format of the units code is as follows:


0 : Special and mathematical units



\begin{picture}(32,3) \put(0,1){\line(1,0){32}} \put(0,3){\line(1,0){32}} \pu... ... \put(7,0){\makebox(9,1)[r]{16}} \put(16,0){\makebox(16,1)[r]{0}} \end{picture}

TYPE
(bits 25 to 28, values 0 to 15) unit type
CAT
(bits 16 to 24, values 0 to 511) unit category
UNIT
(bits 0 to 15, values 0 to 65535) unit


1 : SI base units and dimensionless units from SI base units



\begin{picture}(32,3) \put(0,1){\line(1,0){32}} \put(0,3){\line(1,0){32}} \pu... ... \put(20,0){\makebox(8,1)[r]{4}} \put(28,0){\makebox(4,1)[r]{0}} \end{picture}

BASE
(bits 25 to 28, values 0 to 15) base unit (must be nonzero) 

 		 1 : length 		 $meter$ $m$ 


2 : mass 		 $gram$ $g$ 


3 : time		  $second$ $s$


4 : temperature 		 $kelvin$ $K$


5 : amount of a substance 		 $mole$ $mol$


6 : electrical current 		 $ampere$ $A$


7 : luminous intensity 		 $candela$ $cd$


8 : plane angle 		 $radian$ $rad$


9 : solid angle 		 $steradian$ $sr$
D
(bit 24, values 0 to 1) dimensionless unit flag
0 : specifies a single base quantity
1 : specifies a ratio of quantities with the same BASE
(e.g., $g/kg$)
EXPON
(bits 20 to 23, values 0 to 15) exponent of the base unit. Stored as 8+exponent (e.g., $m^2$ would have EXPON = 10)
PREFIX
(bits 12 to 19, values 0 to 255) prefix for the base unit. Stored as 128+prefix (e.g., $cm$ would have PREFIX = 126). Standard prefixes are:
-18 atto a
-15 femto f
-12 pico p
-9 nano n
-6 micro $\mu$
-3 milli m
-2 centi c
-1 deci d
1 deka da
2 hecto h
3 kilo k
6 mega M
9 giga G
12 tera T
15 peta P
18 exa E
FAC
(bits 4 to 11, values 0 to 255) for dimensionless quantities, the difference between the exponent of the numerator and the exponent of the denominator. Stored as $128+$difference (e.g., $km/cm$ would have FAC $= 128+5 = 133$)
UNIT
(bits 0 to 3, values 0 to 15) for dimensionless quantities, provides an arbitrary index to distinguish between otherwise similar quantities (e.g., $kg/g$ vs. $g/mg$)


2 : SI approved named units



\begin{picture}(32,3) \put(0,1){\line(1,0){32}} \put(0,3){\line(1,0){32}} \pu... ... \put(20,0){\makebox(6,1)[r]{6}} \put(26,0){\makebox(6,1)[r]{0}} \end{picture}

BASE
(bits 20 to 28, values 0 to 511) base units. A bit array that specifies which fundamental SI quantities make up the unit. From LSB to MSB the bit position, the value to add, and the basic units are (bit number, integer value, unit): 

 		 0 		  1 		 length 


1 		  2 		 mass 


2 		  4 		 time


3 		  8 		 temperature


4 		 16 		 amount of a substance


5 		 32 		 electrical current


6 		 64 		 luminous intensity


7 		 128 		 plane angle


8 		 256 		 solid angle
(e.g., $N = kg m/s^{2}; kg = 2, m = 1, s = 4$ so that BASE $= 2 + 1 + 4 = 7$)
PREFIX
(bits 12 to 19, values 0 to 255) prefix for the base unit. Stored as 128+prefix (e.g., $cm$ would have PREFIX = 126). Standard prefixes are given above
CAT
(bits 6 to 11, values 0 to 63) the category of the unit, grouping quantities with the same physical meaning (e.g., $newton$ and $dyne$ would be found in the same category: force)
UNIT
(bits 0 to 5, values 0 to 63) provides an arbitrary index to distinguish between quantities in the same category (e.g., $newton$ vs. $dyne$)


3 : General SI units in terms of base units with restrictions


4 : General non-SI units in terms of base units with restrictions


The structure of both of these forms is the same. Index 3 applies to the SI combination of units, and index 4 applies to any combination of units that include at least one non SI unit. There are certain restrictions in the sizes of the various fields, depending on the number of base units that make up the unit. Any unit that cannot be put into this form should use form 5 (General units without restrictions).


All cases have:



\begin{picture}(32,3) \put(0,1){\line(1,0){12}} \put(0,3){\line(1,0){12}} \pu... ... \put(0,0){\makebox(3,1)[r]{29}} \put(3,0){\makebox(9,1)[r]{20}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(17,0){\makebox(7,1)[r]{8}} \put(24,0){\makebox(8,1)[r]{0}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(20,0){\makebox(5,1)[r]{7}} \put(25,0){\makebox(7,1)[r]{0}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(21,0){\makebox(4,1)[r]{7}} \put(25,0){\makebox(7,1)[r]{0}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(24,0){\makebox(3,1)[r]{5}} \put(27,0){\makebox(5,1)[r]{0}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(22,0){\makebox(4,1)[r]{6}} \put(26,0){\makebox(6,1)[r]{0}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(24,0){\makebox(3,1)[r]{5}} \put(27,0){\makebox(5,1)[r]{0}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(19,0){\makebox(6,1)[r]{7}} \put(25,0){\makebox(7,1)[r]{0}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(20,0){\makebox(5,1)[r]{7}} \put(25,0){\makebox(7,1)[r]{0}} \end{picture}



\begin{picture}(32,3) \put(12,1){\line(1,0){20}} \put(12,3){\line(1,0){20}} \... ... \put(21,0){\makebox(4,1)[r]{7}} \put(25,0){\makebox(7,1)[r]{0}} \end{picture}

BASE
(bits 20 to 28, values 0 to 511) base units. A bit array that specifies which fundamental SI quantities make up the unit. From LSB to MSB the bit position, the value to add, and the basic units are (bit number, integer value, unit): 

 		 0 		  1 		 length 


1 		  2 		 mass 


2 		  4 		 time


3 		  8 		 temperature


4 		 16 		 amount of a substance


5 		 32 		 electrical current


6 		 64 		 luminous intensity


7 		 128 		 plane angle


8 		 256 		 solid angle
(e.g., $N = kg m/s^{2}; kg = 2, m = 1, s = 4$ so that BASE $= 2 + 1 + 4 = 7$)
E$i$
the exponents of the base units. Note that a zero exponent is not included, since it is assumed that the base unit exists if specified. The size and value of the field is variable, depending on the number of base units as follows:
base num bits range exponents
1 15 to 19 0 to 31 -16 to 16
2 12 to 19 0 to 15 -8 to 8
3 11 to 19 0 to 7 -4 to 4
4 8 to 19 0 to 7 -4 to 4
5 10 to 19 0 to 3 -2 to 2
6 8 to 19 0 to 3 -2 to 2
7 13 to 19 0 to 1 -1 or 1
8 12 to 19 0 to 1 -1 or 1
9 11 to 19 0 to 1 -1 or 1
CAT
the category of the unit, grouping quantities with the same physical meaning (e.g., $m/s$ and $cm/s$ would be found in the same category: velocity). The size and value of the field is variable depending on the number of base units as follows:
base num bits range  
1 8 to 14 0 to 127  
2 7 to 11 0 to 31  
3 7 to 10 0 to 15  
4 5 to 7 0 to 7  
5 6 to 9 0 to 15  
6 5 to 7 0 to 7  
7 7 to 12 0 to 63  
8 7 to 11 0 to 31  
9 7 to 10 0 to 15  
UNIT
provides an arbitrary index to distinguish between quantities in the same category (e.g., $m/s$ vs. $cm/s$). The size and value of the field is variable depending on the number of base units as follows:
base num bits range  
1 0 to 7 0 to 255  
2 0 to 6 0 to 127  
3 0 to 6 0 to 127  
4 0 to 4 0 to 31  
5 0 to 5 0 to 63  
6 0 to 4 0 to 31  
7 0 to 6 0 to 127  
8 0 to 6 0 to 127  
9 0 to 6 0 to 127  


5 : General units with no restrictions



\begin{picture}(32,3) \put(0,1){\line(1,0){32}} \put(0,3){\line(1,0){32}} \pu... ... \put(13,0){\makebox(10,1)[r]{9}} \put(23,0){\makebox(9,1)[r]{0}} \end{picture}

BASE
(bits 20 to 28, values 0 to 511) base units. A bit array that specifies which fundamental SI quantities make up the unit. From LSB to MSB the bit position, the value to add, and the basic units are (bit number, integer value, unit): 

 		 0 		  1 		 length 


1 		  2 		 mass 


2 		  4 		 time


3 		  8 		 temperature


4 		 16 		 amount of a substance


5 		 32 		 electrical current


6 		 64 		 luminous intensity


7 		 128 		 plane angle


8 		 256 		 solid angle
(e.g., $mph = 0.447 m/s; m = 1, s = 4$ so that BASE $= 1 + 4 = 7$)
T
(bit 19, values 0 to 1) SI unit indicator
0 : SI unit
1 : non-SI unit
CAT
(bits 9 to 18, values 0 to 1023) the category of the unit, grouping quantities with the same physical meaning (e.g., $mph$ and $fps$ would be found in the same category: velocity)
UNIT
(bits 0 to 8, values 0 to 511) provides an arbitrary index to distinguish between quantities in the same category (e.g., $mph$ vs. $fps$)


7 : Locally defined units

These units are site-defined as specified in Section A.2.5.

next up previous contents
Next: Packing Codes Up: Centrally Defined Codes Previous: Quantity Codes   Contents
Eric Nash 2003-09-25