# Patent

## Title
Optical disc which stores digital information in informational units which diffract a line of laser light at one of 1024 angles and a corresponding light detecting apparatus for reproducing information from said optical disc

## Abstract

The present invention includes an optical disc whose informational units each contain a raised pad designed to reflect laser light at a compound angle which is 45 degrees from the disc surface and at one of 1024 preset angles between 0 and 360 degrees (with 0 degrees being oriented radially towards the disc center). Light reflected from the information units intersects with a ring of light detecting receptors arranged circumferentially around the laser/light source. When individual receptors are struck by reflected laser light: a signal is sent to a processor. This processor determines the order in which the receptors are stuck and outputs integers. Each integer corresponds to the receptor that was struck and this data, when streamed sequentially, reproduces the data stored on the optical disc.

## Background
BACKGROUND OF THE INVENTION
1. Field of Invention
The invention relates to optical discs used to store digital information and corresponding optical discs drives used to reproduce data from such discs.
2. Description of Prior Art
The optical disc and corresponding disc reading apparatus of the present invention are a divergence from other forms of laser read optical media including optical discs such as the Video Disc, the Compact Disc (CD-ROM) with associated drive and the Digital Video Disc (DVD-ROM) with its associated drive. A brief description of these will be set forth in the following paragraphs.
Compact discs (CDs) or Compact Disc-Read Only Memory (CD-ROM) are currently available with a capacity of 640 M bytes. The CD-ROM drive reads data in binary format from a number of pits and stripes arranged on the reflective surface of the compact disc (CD). If the laser signal strikes a stripe on the CD surface and is reflected back toward the source it is routed to a receptor head and interpreted as the number 1. If the signal is not reflected back (due to the presence of a pit on the surface of the disc) and is not routed to the receptor head, the output is a 0. In this manner, data is encoded onto the disc in binary format. (See FIGS. 1 and 2)
Digital Video Discs (DVDs) have an increased capacity over CDs, storing up to 4.7 G bytes of data per disc. The drive still reads in binary, as with its CD predecessor, however, the DVD achieves the much larger capacity by placing the data pits on the disc surface closer together and by arranging them such that two different wavelengths of laser light read two separate layers of data. DVDs function much the same as CDs in that the laser light is directed at the surface of the disc and if reflected back toward the source a 1 is interpreted and if not reflected a 0 is interpreted, thus storing and retrieving data in binary format. (Similar to the CD illustrated in FIGS. 1 and 2)
Subsequent to the drives described previously, optical discs have been designed which store digital information in a plurality of pits within a single informational unit, instead of a single pit (or the absence thereof) in each informational unit on the disc. By creating varied patterns of pits, the light reflected back from the disc creates patterns of light intensity that are interpreted to reproduce the data from the disc. Diffraction gratings have also been used to reflect incident light to a number of receptors.
The present invention differs from prior art in that it uses raised pads to store information rather than pits (whether singular in each informational unit or plural) or diffraction gratings which allows the present invention to reflect light to an exponentially larger number of receptors. It also diverges from previous inventions in its use of a receptor ring that surrounds and is attached to the laser light source and moves with the said source in order to maintain constant distance and angle between the light source, the informational unit being read from the disc surface and the receptors in the ring.
And lastly, the present invention differs from previous inventions in that the receptors in the ring are dynamically interpreted by a processor and can be combined to form logical receptors as noted in claim 8 of the present invention.
Other optical discs have been patented which store digital information in a plurality of pits within a single informational unit, instead of a single pit (or the absence thereof) in each informational unit on the discs. By creating varied patterns of pits, the light reflected back from the disc creates patterns of light intensity that are interpreted to reproduce the data from the disc.
Others have used diffraction gratings to reflect incident light to a number of receptors. The present invention differs from prior art in that it uses raised pads to store information rather than pits (whether singular in each informational unit of plural) or diffraction gratings. It also diverges from previous inventions in its use of a receptor ring that surrounds and is attached to the laser light source and moves with the said source in order to maintain constant distance and angle between the light source, the informational unit being read from the disc surface and the receptors in the ring. And lastly, the present invention differs from previous inventions in that the receptors in the ring are dynamically interpreted by a processor and can be combined to form logical receptors as noted in claim 3 of the present invention.
The object of the present invention is to set forth an optical disc device (and associated optical disc) that is capable of reading data that is stored in higher level number systems (Octal, Hexadecimal. etc. up to 1 kbit or higher) in order to store data very densely on the disc by utilizing a raised pad, rather than a pit or pattern of pits, in each of the informational units on the disc. These raised pacts reflect light in a straight line at one of 1024 angles so as to strike one (or a logical grouping) of the 1024 receptors in a receptor ring that is arranged circumferentially around and attached to the laser source. The receptor ring moves with tile laser light source as it moves in its path radially along the disc surface and maintains constant distances between the light source, the disc surface (and informational units thereon) and the receptor ring.
The second object of the present invention is to provide an apparatus for reproducing information from the disc noted in the first object, by sequentially irradiating the raised pads in the information units on the disc with laser light and by detecting the light reflected back from these raised pads to a ring of receptors that is arranged circumferentially around the laser light source and attached to the same source so that it moves with the light source as the disc is read. When a receptor in this ring is irradiated by light reflected from the disc, a signal is sent to a processor which outputs an integer that corresponds to the individual receptor that generated the signal. Therefore the angle of reflection of each pad on the disc corresponds to a particular receptor in the ring, which when irradiated generates a signal that causes the processor to output an integer corresponding to the receptor. Thus, due to the angle of each pad, each informational unit stores an integer that can be read and output sequentially by the apparatus.
It is the third object of the present invention to provide an apparatus according to the second object which combines groups of adjacent receptors to form logical receptors in order to increase the size of the receptor to decrease the complexity (and associated production expenses and intricacies) but which also decreases the overall capacity of the disc. This is done by the processor (noted in the preceding paragraph), which determines the order in which receptors are irradiated with light. When combining physical receptors into logical receptors, the processor accepts signals from any receptor in a logical group as being from a single receptor and outputs an integer associated with the group rather than the integer associated with tile individual receptor. Thus a number of physical receptors are combined to form a single logical receptor dynamically.
SUMMARY OF THE INVENTION
According to the present invention, an optical disc is used to store data that is read by a laser in much the same way as with previous optical discs. However, according to the present invention, the data locations on the disc surface are raised pads that reflect the laser light at a compound angle comprised of the following two angles

    
    
        1. An angle of 45° from the disc surface.
        2. At one of several pre-set angles from the center of the laser read head (with zero degrees oriented toward the center of the disc).
    
    


The number of pre-set angles determines the number of variables that can be stored at each data location on the disc. On discs storing data in the octal number system there are 8 pre-set angles, on discs storing data in hexadecimal there are 16 pre-set angles, and so on.
The disc drive used to read from the said optical media, according to the present invention, contains a ring of receptors that is arranged concentrically around the laser light source and is attached to this laser source so as to move with it and remain at a constant distance from the laser source and at a constant distance from the disc surface. There are 1024 individual receptors that can act separately or that can be grouped to form larger logical heads (grouping to form logical receptors is described in greater detail in the following section). In this manner, if the optical disc being read contains data stored with 1024 pre-set angles, the drive utilizes each of the 1024 receptors individually. If the disc being read by the drive contains data stored with 8 preset angles, groups of adjacent heads combine to form 8 logical receptors. Thus the disc and chive are able to store and retrieve data in any number system from octal (8-bit) to 1024 (1 kilobit).
Receptor Grouping/Logical Receptors
As mentioned above, the ring of 1024 receptors is dynamic and can act as 1024 individual receptors or can combine adjacent receptors into groups to form logical receptors (or heads). This dynamic grouping allows the drive to read discs with varying capacities and provides manufacturers with production cost options. Discs with smaller amounts of data can utilize lower number systems and costs can be lowered, and discs that contain greater amounts of data can justify the cost of utilizing higher systems.
The drive can dynamically combine adjacent to heads to form 8, 16, 32, 64, 128, 256 or 512 logical receptors according to the following.
8 logical heads are formed by combining groups of 128 adjacent receptors into each logical receptor. The particular receptors (or heads) that are contained in each group and the location of the group in degrees from the laser center (with zero oriented toward the disc center) are outlined in TABLE 1 and illustrated in FIG. 6.
16 logical heads are formed by combining groups of 64 adjacent receptors into each logical receptor. The particular receptors (or heads) that are contained in each group and the location of the group in degrees from the laser center (with zero oriented toward the disc center) are outlined in TABLE 2.
32 logical heads are formed by combining groups of 32 adjacent receptors into each logical receptor. The particular receptors (or heads) that are contained in each group and the location of the group in degrees from the laser center (with zero oriented toward the disc center) are outlined in TABLE 3.
64 logical heads are formed by combining groups of 16 adjacent receptors into each logical receptor. The particular receptors (or heads) that are contained in each group and the location of the group in degrees from the laser center (with zero oriented toward the disc center) are outlined in TABLE 4.
128 logical heads are formed by combining groups of 8 adjacent receptors into each logical receptor. The particular receptors (or heads) that are contained in each group and the location of the group in degrees from the laser center (with zero oriented toward the disc center) are outlined in TABLE 5.
256 logical heads are formed by combining groups of 4 adjacent receptors into each logical receptor. The particular receptors (or heads) that are contained in each group and the location of the group in degrees from the laser center (with zero oriented toward the disc center) are outlined in TABLE 6.
512 logical heads are formed by combining groups of 2 adjacent receptors into each logical receptor. The particular receptors (or heads) that are contained in each group and the location of the group in degrees from the laser center (with zero oriented toward the disc center) are outlined in TABLE 7.
1024 heads are available if each receptor acts as an individual head. The locations of the individual heads in degrees from the laser center (with zero oriented toward the disc center) are outlined in Table 8.
Accordingly therefore, as a point of example, if a disc contains data written in the above said 8-bit format and laser light is reflected from the disc surface at some angle between 0 and 44 degrees, striking the receptor ring in the range of receptors 0-127, the output of the drive would be 1. And if the laser light is reflected at some angle between 45 and 89 degrees striking the receptor ring in the range of receptors 128-255 the output would be a 2. And so on for each logical location according to Table 1.
Expandability
Since the Dynamic Disc derives its increased capacity from the large number of variables possible at each data location on the disc, the overall capacity of the disc (and drive) can be expanded by increasing the number of receptor heads in the receptor ring (ie to 2048, 4096, etc), and correspondingly creating discs that reflect more highly focused and directed laser light to strike the increased number of receptors. And if technology becomes such that the laser can be reflected as a fine dot rather than as a line, several concentric rings of receptors could be placed around the laser, increasing the capacity and capabilities of the disc astronomically.















Disc resolution
Number length
Possible Combinations









Binary (CD/DVD)
 40-bit
240 or 1.1 × 1012




128-bit
2128 or 3.4 × 1038



Octal
 40-bit
840 or 1.3 × 1036




128-bit
8128 or 3.9 × 10115



32-bit
 40-bit
3240 or 1.6 × 1060




128-bit
32128 or 4.6 × 10192



1024
 40-bit
102440 or 2.6 × 10120




128-bit
1024128 or 2.1 × 10385










Software Driver
The Dynamic Disc Drive reads the data from the Dynamic Drive Disc and sends only integers to the computer for processing. Decoding of the integers from the drive takes place on the computer (not on the Dynamic Drive). This allows software drivers to interpret the same data differently from different discs. The software component of the DDD driver will contain interpretive sets. For example, the number 672 sent from a C++ program disc in the DDD to the computer could represent a C++ command or subroutine while the same number (672) coming from a computer game DDD could represent the movement of a character, or a particular command relative to the games code. The possibilities are virtually innumerable.
Additional interpretive sets could be added dynamically to the driver for new additions from particular vendors who wish to capitalize on the new technology by creating their own sets. If the set on the disc is not part of the driver currently loaded, the set could be copied from the disc to the driver or downloaded from the internet and added to the driver. The interpretive set used to decode any particular disc is determined during the handshaking session between the Dynamic Disc and the Dynamic Drive when the disc is first inserted into the drive. Handshaking will be discussed in more detail hereafter.
Handshaking
Since there are to be numerous interpretive sets used to decode the DDD data, and there are numerous disc resolutions possible on the DDD, a handshaking session is necessary. When the Dynamic disc is first inserted into the Dynamically Divisible Drive, the drive reads the first few rings of data which are written in binary format. The data contained in the said rings indicates whether or not the disc is a Dynamic Drive Disc. If there is no handshaking data then the drive recognizes the disc as a CD or a DVD. If handshaking data is encountered, the drive reads the data to determine the following:

    
    
        1. The disc resolution.
        
            The drive determines whether the DDD contains 8, 16, 32, 64, 128, 256, 512, or 1024 bit data and groups the receptors into logical heads accordingly.
        
        
        2. The interpretive set to be used.
        
            As mentioned above, various interpretive sets can be used to interpret the integers sent from the disc to the computer. The handshaking session determines which set is to be used for the particular disc in the drive.
        
        
        3. Where a non-standard interpretive set can be found.
        
            If the set to be used is not one of the standard sets included with the original driver, the disc handshaking will indicate if its interpretive set is included on the disc in binary format to be copied to the driver on the computer or will give the location for downloading the set from the manufacturer.
        
        
    
    


The drive is thereby able to determine the properties of each individual disc inserted and manufacturers are presented with the freedom to develop sets that meet the need of their particular industry.
Dynamic Drive Disc
The Dynamic Drive Disc is similar to its predecessors (CD and DVD) in that it is made of a plastic disc with a reflective coating covered by a protective finish. The reflective coating may be a malleable substance that can be stamped with the various reflective pads in a manner opposite to the pits and stripes are stamped into other optical discs. Rather than stamping holes or concave shapes into the disc surface, the area around tile reflective pad is depressed leaving a raised pad in the informational unit which directs light away from the laser source to the ring of receptors arranged around the laser. Or the disc surface may consist of a material that can be engraved by a highly focused laser system designed specifically for writing to tile disc media of the present invention.



DESCRIPTION OF THE DRAWINGS
The figures contained herein are intended to illustrate the concepts outlined in the present invention and are not and weren't intended as representations of the actual devices described.
FIG. 1 illustrates the basic operation of the legacy compact disc in which the laser is directed at the surface of the optical disc which reflects the laser back toward the source (due to the presence of a stripe on the disc surface). The laser is then routed by a mirror to a receptor and the output of the read cycle is a binary 1.
FIG. 2 also illustrates the basic function of the legacy compact disc, however, in this illustration the laser is scattered by the presence of a pit on the disc surface. No light is directed to the receptor and the output of the read cycle is a binary 0.
FIG. 3 illustrates the basic function of the Dynamic Disc Drive. Laser light is directed at the surface of the disc and is reflected to one of the receptors in the receptor ring. In contrast to FIGS. 1 and 2 there are numerous possible receptors to which the laser can be directed (only one of the numerous possible reflections is shown). The output for this read cycle is the integer that corresponds with the receptor that was struck by the reflected laser light. Also note that the binary receptor is still present allowing for backward compatibility enabling the drive to read compact and digital versatile discs in addition to the Dynamic Drive Discs.
FIG. 4 illustrates a simplified top view of the Dynamic Drive laser and receptor ring.
The laser light is reflected outward from the disc surface in a line that strikes an area on the receptor ring. The receptor (or receptors) struck output an integer. The integer varies according to the logical grouping used. Angles for the locations of these groups, the receptors or heads in each group and the corresponding output (integer) are found in Tables 1 through 8.
FIG. 5 illustrates the various reflection patterns produced by discs containing different number systems.
FIG. 5a illustrates the broad, less focused pattern of an octal or a hexadecimal type disc. The broad pattern requires the combination of large numbers of receptors into logical heads to avoid overlap and error.
FIG. 5b illustrates a more highly focused pattern that would be typical of the mid-range discs (128-bit to 256-bit discs, for example). The narrower pattern still requires the combination of receptors into logical heads, but because it is much narrower than the previous example, less receptors are required for each logical group allowing for a larger number of groups.
FIG. 5c illustrates an even more highly focused pattern that would be typical of the highest capacity discs (512-bit and 1024-bit). The highly focused pattern strikes only one or two receptors requiring minimal or no grouping of receptors.
FIG. 6 is a graphical representation of the data in Table 1. The laser is in the center surrounded by the ring of 1024 receptor heads. Section 1 is from 0 to 44 degrees and is comprised of heads 0 through 127. If laser light is directed to any of the receptors in this section from the disc surface, the output for the read cycle is a 1. Each subsequent section contains the location in degrees, the heads contained in the group and the corresponding output for that section.



DESCRIPTION OF THE TABLES
Eight tables are included herewith. The tables indicate the location of the logical receptors for each possible subdivision of the receptor ring. The location is given in a range of degrees from 0 to 359 with 0 oriented toward the center of the disc. The tables also note which of the 1024 heads in the receptor ring are included in each logical head. The heads are numbered with head 0 being the head at 0 degrees (in a straight line from the center of the laser head to the center of the disc).
The tables are as follows:
TABLE 1 outlines the 8-bit division of the ring
TABLE 2 outlines the 16-bit division of the ring
TABLE 3 outlines the 32-bit division of the ring
TABLE 4 outlines the 64-bit division of the ring
TABLE 5 outlines the 128-bit division of the ring
TABLE 6 outlines the 256-bit division of the ring
TABLE 7 outlines the 512-bit division of the ring
TABLE 8 outlines the 1024-bit division of the ring







TABLE 1







8-bit Division










logical head
Heads in Group (128


Integer sent
location (degrees
head grouping = 1 logical


to processor
from center)
head)





0
None (0 = no
None



reflection)


1
0-44 degrees
Heads 0-127


2
45-89 degrees
heads 128-255


3
90-134 degrees
heads 256-383


4
135-179 degrees
heads 384-511


5
180-224 degrees
heads 512-639


6
225-269 degrees
heads 640-767


7
270-314 degrees
heads 768-895


8
315-359 degrees
heads 896-1023
















TABLE 2







16-bit Division









Integer sent
logical head
Heads in Group (64


to
location (degrees
head grouping = 1 logical


processor
from center)
head)












0
No reflection from
None



disk


1
0-22 degrees
Heads 0-63 in group


2
22.5-44.5 degrees
Heads 64-127 in group


3
45-67 degrees
Heads 128-191 in group


4
67.5-89.5 degrees
Heads 192-255 in group


5
90-112 degrees
Heads 256-319 in group


6
112.5-134.5 degrees
Heads 320-383 in group


7
135-157 degrees
Heads 384-447 in group


8
157.5-179.5 degrees
Heads 448-511 in group


9
180-202 degrees
Heads 512-575 in group


10
202.5-224.5 degrees
Heads 576-639 in group


11
225-247 degrees
Heads 640-703 in group


12
247.5-269.5 degrees
Heads 704-767 in group


13
270-292 degrees
Heads 768-831 in group


14
292.5-314.5 degrees
Heads 832-895 in group


15
315-337 degrees
Heads 896-959 in group


16
337.5-359-5 degrees
Heads 960-1023 in group
















TABLE 3







32-bit Division









Integer




sent to
logical head location
Heads in Group (32 head


processor
(degrees from center)
grouping = 1 logical head)












0
No reflection from disk
none


1
0 through 11 degrees
Heads 0-31 in group


2
11.25 through 22.25 degrees
Heads 32-63 in group


3
22.5 through 33.5 degrees
Heads 64-95 in group


4
33.75 through 44.75 degrees
Heads 96-127 in group


5
45 through 56 degrees
Heads 128-159 in group


6
56.25 through 67.25 degrees
Heads 160-191 in group


7
67.5 through 78.5 degrees
Heads 192-223 in group


8
78.75 through 89.75 degrees
Heads 224-255 in group


9
90 through 101 degrees
Heads 256-287 in group


10
101.25 through 112.25 degrees
Heads 288-319 in group


11
112.5 through 123.5 degrees
Heads 320-351 in group


12
123.75 through 134.75 degrees
Heads 352-383 in group


13
135 through 146 degrees
Heads 384-415 in group


14
146.25 through 157-25 degrees
Heads 416-447 in group


15
157.5 through 168.5 degrees
Heads 448-479 in group


16
168.75 through 179.75 degrees
Heads 480-511 in group


17
180 through 191 degrees
Heads 512-543 in group


18
191.25 through 202.25 degrees
Heads 544-575 in group


19
202.5 through 213.5 degrees
Heads 576-607 in group


20
213.75 through 224.75 degrees
Heads 608-639 in group


21
225 through 236 degrees
Heads 640-671 in group


22
236.25 through 247.25 degrees
Heads 672-703 in group


23
247.5 through 258.5 degrees
Heads 704-735 in group


24
258.75 through 269.75 degrees
Heads 736-767 in group


25
270 through 281 degrees
Heads 768-799 in group


26
281.25 through 292.25 degrees
Heads 800-831 in group


27
292.5 through 303-5 degrees
Heads 832-863 in group


28
303.75 through 314.75 degrees
Heads 864-895 in group


29
315 through 326 degrees
Heads 896-927 in group


30
326.25 through 337.25 degrees
Heads 928-959 in group


31
337.5 through 348.5 degrees
Heads 960-991 in group


32
348.75 through 359.75 degrees
Heads 992-1023 in group
















TABLE 4







64-bit Division









Integer




sent to
logical head location
Heads in Group (16 head


processor
(degrees from center)
grouping = 1 logical head)












0
No reflection
None


1
   0 through 5.5 degrees
Heads 0-15 in group


2
 5.63 through 11.13 degrees
Heads 16-31 in group


3
 11.25 through 16.75 degrees
Heads 32-47 in group


4
 16.88 through 22.38 degrees
Heads 48-63 in group


5
 22.5 through 28 degrees
Heads 64-79 in group


6
 28.13 through 33.63 degrees
Heads 80-95 in group


7
 33.75 through 39.25 degrees
Heads 96-111 in group


8
 39.38 through 39.88 degrees
Heads 112-127 in group


9
   45 through 50.5 degrees
Heads 128-143 in group


10
 50.63 through 56.13 degrees
Heads 144-159 in group


11
 56.25 through 61.75 degrees
Heads 160-175 in group


12
 61.88 through 67.38 degrees
Heads 176-191 in group


13
 67.5 through 73 degrees
Heads 192-207 in group


14
 73.13 through 78.63 degrees
Heads 208-223 in group


15
 78.75 through 84.25 degrees
Heads 224-239 in group


16
 84.38 through 89.88 degrees
Heads 240-255 in group


17
   90 through 95.5 degrees
Heads 256-271 in group


18
 95.63 through 101.13 degrees
Heads 272-287 in group


19
101.25 through 106.75 degrees
Heads 288-303 in group


20
106.88 through 112.38 degrees
Heads 304-319 in group


21
 112.5 through 118 degrees
Heads 320-335 in group


22
118.13 through 123.63 degrees
Heads 336-351 in group


23
123.75 through 129.25 degrees
Heads 352-367 in group


24
129.38 through 134.88 degrees
Heads 368-383 in group


25
  135 through 140.5 degrees
Heads 384-399 in group


26
140.63 through 146.13 degrees
Heads 400-415 in group


27
146.25 through 151.75 degrees
Heads 416-431 in group


28
151.88 through 157.38 degrees
Heads 432-447 in group


29
 157.5 through 163 degrees
Heads 448-463 in group


30
163.13 through 168.63 degrees
Heads 464-479 in group


31
168.75 through 174.25 degrees
Heads 480-495 in group


32
174.38 through 179.88 degrees
Heads 496-511 in group


33
  180 through 185.5 degrees
Heads 512-527 in group


34
185.63 through 191.13 degrees
Heads 528-543 in group


35
191.25 through 196.75 degrees
Heads 544-559 in group


36
196.88 through 202.38 degrees
Heads 560-575 in group


37
 202.5 through 208 degrees
Heads 576-591 in group


38
208.13 through 213.63 degrees
Heads 592-607 in group


39
213.75 through 219.25 degrees
Heads 608-623 in group


40
219.38 through 224.88 degrees
Heads 624-639 in group


41
  225 through 230.5 degrees
Heads 640-655 in group


42
230.63 through 236.13 degrees
Heads 656-671 in group


43
236.25 through 241.75 degrees
Heads 672-687 in group


44
241.88 through 247.38 degrees
Heads 688-703 in group


45
 247.5 through 253 degrees
Heads 704-719 in group


46
253.13 through 258.63 degrees
Heads 720-735 in group


47
258.75 through 264.25 degrees
Heads 736-751 in group


48
264.38 through 269.88 degrees
Heads 752-767 in group


49
  270 through 275.5 degrees
Heads 768-783 in group


50
275.63 through 281.13 degrees
Heads 784-799 in group


51
281.25 through 286.75 degrees
Heads 800-815 in group


52
286.88 through 292.38 degrees
Heads 816-831 in group


53
 292.5 through 298 degrees
Heads 832-847 in group


54
298.13 through 303.63 degrees
Heads 848-863 in group


55
303.75 through 309.25 degrees
Heads 864-879 in group


56
309.38 through 314.88 degrees
Heads 880-895 in group


57
  315 through 320.5 degrees
Heads 896-911 in group


58
320.63 through 326.13 degrees
Heads 912-927 in group


59
326.25 through 331.75 degrees
Heads 928-943 in group


60
331.88 through 337.38 degrees
Heads 944-959 in group


61
 337.5 through 343 degrees
Heads 960-975 in group


62
343.13 through 348.63 degrees
Heads 976-991 in group


63
348.75 through 354.25 degrees
Heads 992-1007 in group


64
354.38 through 359.88 degrees
Heads 1008-1023 in group
















TABLE 5







128-bit Division









Integer




sent to
logical head location
Heads in Group (8 head


processor
(degrees from center)
grouping = 1 logical head)













0
None

None


1
0-2.75
degrees
Heads 0-7 in group


2
2.813-5.563
degrees
Heads 8-15 in group


3
5.625-8.375
degrees
Heads 16-23 in group


4
8.438-11.188
degrees
Heads 24-31 in group


5
11.25-14
degrees
Heads 32-39 in group


6
14.063-16.813
degrees
Heads 40-47 in group


7
16.875-19.625
degrees
Heads 48-55 in group


8
19.688-22.438
degrees
Heads 56-63 in group


9
22.5-25.25
degrees
Heads 64-71 in group


10
25.313-28.063
degrees
Heads 72-79 in group


11
28.125-30.875
degrees
Heads 80-87 in group


12
30.938-33.688
degrees
Heads 88-95 in group


13
33.75-36.5
degrees
Heads 96-103 in group


14
36.563-39.313
degrees
Heads 104-111 in group


15
39.375-42.125
degrees
Heads 112-119 in group


16
42.188-44.938
degrees
Heads 120-127 in group


17
45-47.75
degrees
Heads 128-135 in group


18
47.813-50.563
degrees
Heads 136-143 in group


19
50.625-53.375
degrees
Heads 144-151 in group


20
53.438-56.188
degrees
Heads 152-159 in group


21
56.25-59
degrees
Heads 160-167 in group


22
59.063-61.813
degrees
Heads 168-175 in group


23
61.875-64.625
degrees
Heads 176-183 in group


24
64.688-67.438
degrees
Heads 184-191 in group


25
67.5-70.25
degrees
Heads 192-199 in group


26
70.313-73.063
degrees
Heads 200-207 in group


27
73.125-75.875
degrees
Heads 208-215 in group


28
75.938-78.688
degrees
Heads 216-223 in group


29
78.75-81.5
degrees
Heads 224-231 in group


30
81.563-84.313
degrees
Heads 232-239 in group


31
84.375-87.125
degrees
Heads 240-247 in group


32
87.188-89.938
degrees
Heads 248-255 in group


33
90-92.75
degrees
Heads 256-263 in group


34
92.813-95.563
degrees
Heads 264-271 in group


35
95.625-98.375
degrees
Heads 272-279 in group


36
98.438-101.188
degrees
Heads 280-287 in group


37
101.25-104
degrees
Heads 288-295 in group


38
104.063-106.813
degrees
Heads 296-303 in group


39
106.875-109.625
degrees
Heads 304-311 in group


40
109.688-112.438
degrees
Heads 312-319 in group


41
112.5-115.25
degrees
Heads 320-327 in group


42
115.313-118.063
degrees
Heads 328-335 in group


43
118.125-120.875
degrees
Heads 336-343 in group


44
120.938-123.688
degrees
Heads 344-351 in group


45
123.75-126.5
degrees
Heads 352-359 in group


46
126.563-129.313
degrees
Heads 360-367 in group


47
129.375-132.125
degrees
Heads 368-375 in group


48
132.188-134.938
degrees
Heads 376-383 in group


49
135-137.75
degrees
Heads 384-391 in group


50
137.813-140.563
degrees
Heads 392-399 in group


51
140.625-143.375
degrees
Heads 400-407 in group


52
143.438-146.188
degrees
Heads 408-415 in group


53
146.25-149
degrees
Heads 416-423 in group


54
149.063-151.813
degrees
Heads 424-431 in group


55
151.875-154.625
degrees
Heads 432-439 in group


56
154.688-157.438
degrees
Heads 440-447 in group


57
157.5-160.25
degrees
Heads 448-455 in group


58
160.313-163.063
degrees
Heads 456-463 in group


59
163.125-165.875
degrees
Heads 464-471 in group


60
165.938-168-688
degrees
Heads 472-479 in group


61
168.75-171.5
degrees
Heads 480-487 in group


62
171.563-174.313
degrees
Heads 488-495 in group


63
174.375-177.125
degrees
Heads 496-503 in group


64
177.188-179.938
degrees
Heads 504-511 in group


65
180-182.75
degrees
Heads 512-519 in group


66
182.813-185.563
degrees
Heads 520-527 in group


67
185.625-188.375
degrees
Heads 528-535 in group


68
188.438-191.188
degrees
Heads 536-543 in group


69
191.25-194
degrees
Heads 544-551 in group


70
194.063-196.813
degrees
Heads 552-559 in group


71
196.875-199.625
degrees
Heads 560-567 in group


72
199.688-202.438
degrees
Heads 568-575 in group


73
202.5-205.25
degrees
Heads 576-583 in group


74
205.313-208.063
degrees
Heads 584-591 in group


75
208.125-210.875
degrees
Heads 592-599 in group


76
210.938-213.688
degrees
Heads 600-607 in group


77
213.75-216.5
degrees
Heads 608-615 in group


78
216.563-219.313
degrees
Heads 616-623 in group


79
219.375-222.125
degrees
Heads 624-631 in group


80
222.188-224.938
degrees
Heads 632-639 in group


81
225-227.75
degrees
Heads 640-647 in group


82
227.813-230.563
degrees
Heads 648-655 in group


83
230.625-233.375
degrees
Heads 656-663 in group


84
233.438-236.188
degrees
Heads 664-671 in group


85
236.25-239
degrees
Heads 672-679 in group


86
239.063-241.813
degrees
Heads 680-687 in group


87
241.875-244.625
degrees
Heads 688-695 in group


88
244.688-247.438
degrees
Heads 696-703 in group


89
247.5-250.25
degrees
Heads 704-711 in group


90
250.313-253.063
degrees
Heads 712-719 in group


91
253.125-255.875
degrees
Heads 720-727 in group


92
255.938-258.688
degrees
Heads 728-735 in group


93
258.75-261.5
degrees
Heads 736-743 in group


94
261.563-264.313
degrees
Heads 744-751 in group


95
264.375-267.125
degrees
Heads 752-759 in group


96
267.188-269.938
degrees
Heads 760-767 in group


97
270-272.75
degrees
Heads 768-775 in group


98
272.813-275.563
degrees
Heads 776-783 in group


99
275.625-278.375
degrees
Heads 784-791 in group


100
278.438-281.188
degrees
Heads 792-799 in group


101
281.25-284
degrees
Heads 800-807 in group


102
284.063-286.813
degrees
Heads 808-815 in group


103
286.875-289.625
degrees
Heads 816-823 in group


104
289.688-292.438
degrees
Heads 824-831 in group


105
292.5-295.25
degrees
Heads 832-839 in group


106
295.313-298.063
degrees
Heads 840-847 in group


107
298.125-300.875
degrees
Heads 848-855 in group


108
300.938-303.688
degrees
Heads 856-863 in group


109
303.75-306.5
degrees
Heads 864-871 in group


110
306.563-309.313
degrees
Heads 872-879 in group


111
309.375-312.125
degrees
Heads 880-887 in group


112
312.188-314.938
degrees
Heads 888-895 in group


113
315-317.75
degrees
Heads 896-903 in group


114
317.813-320.563
degrees
Heads 904-911 in group


115
320.625-323.375
degrees
Heads 912-919 in group


116
323.438-326.188
degrees
Heads 920-927 in group


117
326.25-329
degrees
Heads 928-935 in group


118
329.063-331.813
degrees
Heads 936-943 in group


119
331.875-334.625
degrees
Heads 944-951 in group


120
334.688-337.438
degrees
Heads 952-959 in group


121
337.5-340.25
degrees
Heads 960-967 in group


122
340.313-343.063
degrees
Heads 968-975 in group


123
343.125-345.875
degrees
Heads 976-983 in group


124
345.938-348.688
degrees
Heads 984-991 in group


125
348.75-351.5
degrees
Heads 992-999 in group


126
351.563-354.313
degrees
Heads 1000-1007 in group


127
354.375-357.125
degrees
Heads 1008-1015 in group


128
357.188-359.938
degrees
Heads 1016-1023 in group
















TABLE 6







256-bit Division









Integer




sent to
logical head location
Heads in Group (4 head


processor
(degrees from center)
grouping = 1 logical head)












0
None
None


1
   0 through 1.38 degrees
0 through 3


2
 1.41 through 2.78 degrees
4 through 7


3
 2.82 through 4.19 degrees
 8 through 11


4
 4.22 through 5.59 degrees
12 through 15


5
 5.62 through 7 degrees
16 through 19


6
 7.03 through 8.41 degrees
20 through 23


7
 8.44 through 9.81 degrees
24 through 27


8
 9.84 through 11.22 degrees
28 through 31


9
 11.25 through 12.63 degrees
32 through 35


10
 12.66 through 14.03 degrees
36 through 39


11
 14.06 through 15.44 degrees
40 through 43


12
 15.47 through 16.84 degrees
44 through 47


13
 16.87 through 18.25 degrees
48 through 51


14
 18.28 through 19.66 degrees
52 through 55


15
 19.69 through 21.06 degrees
56 through 59


16
 21.09 through 22.47 degrees
60 through 63


17
 22.50 through 23.88 degrees
64 through 67


18
 23.91 through 25.28 degrees
68 through 71


19
 25.31 through 26.69 degrees
72 through 75


20
 26.72 through 28.09 degrees
76 through 79


21
 28.12 through 29.50 degrees
80 through 83


22
 29.53 through 30.91 degrees
84 through 87


23
 30.94 through 32.31 degrees
88 through 91


24
 32.34 through 33.72 degrees
92 through 95


25
 33.75 through 35.13 degrees
96 through 99


26
 35.16 through 36.53 degrees
100 through 103


27
 36.56 through 37.94 degrees
104 through 107


28
 37.97 through 39.34 degrees
108 through 113


29
 39.37 through 40.75 degrees
112 through 115


30
 40.78 through 42.16 degrees
116 through 119


31
 42.19 through 43.56 degrees
120 through 123


32
 43.59 through 44.97 degrees
124 through 127


33
   45 through 46.38 degrees
128 through 131


34
 46.41 through 47.78 degrees
132 through 135


35
 47.81 through 49.19 degrees
136 through 139


36
 49.22 through 50.59 degrees
140 through 143


37
 50.62 through 52 degrees
144 through 147


38
 52.03 through 54.41 degrees
148 through 151


39
 53.44 through 54.81 degrees
152 through 155


40
 54.84 through 56.22 degrees
156 through 159


41
 56.25 through 57.63 degrees
160 through 163


42
 57.66 through 59.03 degrees
164 through 167


43
 59.06 through 60.44 degrees
168 through 171


44
 60.47 through 61.84 degrees
172 through 175


45
 61.87 through 63.25 degrees
176 through 179


46
 63.28 through 64.66 degrees
180 through 183


47
 64.69 through 66.06 degrees
184 through 187


48
 66.09 through 67.47 degrees
188 through 191


49
 67.5 through 68.88 degrees
192 through 195


50
 68.91 through 70.28 degrees
196 through 199


51
 70.31 through 71.69 degrees
200 through 203


52
 71.72 through 73.09 degrees
204 through 207


53
 73.12 through 74.5 degrees
208 through 211


54
 74.53 through 75.91 degrees
212 through 215


55
 75.94 through 77.31 degrees
216 through 219


56
 77.34 through 78.72 degrees
220 through 223


57
 78.75 through 80.13 degrees
224 through 227


58
 80.16 through 81.53 degrees
228 through 231


59
 81.56 through 82.94 degrees
232 through 235


60
 82.97 through 84.34 degrees
236 through 239


61
 84.37 through 85.75 degrees
240 through 243


62
 85.78 through 87.16 degrees
244 through 247


63
 87.19 through 88.56 degrees
248 through 251


64
 88.59 through 89.97 degrees
252 through 255


65
   90 through 91.38 degrees
256 through 259


66
 91.41 through 92.78 degrees
260 through 263


67
 92.81 through 94.19 degrees
264 through 267


68
 94.22 through 95.59 degrees
268 through 271


69
 95.62 through 97 degrees
272 through 275


70
 97.03 through 98.41 degrees
276 through 279


71
 98.44 through 99.81 degrees
280 through 283


72
 99.84 through 101.22 degrees
284 through 287


73
101.25 through 102.63 degrees
288 through 291


74
102.66 through 104.03 degrees
292 through 295


75
104.06 through 105.44 degrees
296 through 299


76
105.47 through 106.84 degrees
300 through 303


77
106.87 through 108.25 degrees
304 through 307


78
108.28 through 109.66 degrees
308 through 311


79
109.69 through 111.06 degrees
312 through 315


80
111.09 through 112.47 degrees
316 through 319


81
 112.5 through 113.88 degrees
320 through 323


82
113.91 through 115.28 degrees
324 through 327


83
115.31 through 116.69 degrees
328 through 331


84
116.72 through 118.09 degrees
332 through 335


85
118.12 through 119.5 degrees
336 through 339


86
119.53 through 120.91 degrees
340 through 343


87
120.94 through 122.31 degrees
344 through 347


88
122.34 through 123.72 degrees
348 through 351


89
123.75 through 125.13 degrees
352 through 355


90
125.16 through 126.53 degrees
356 through 359


91
126.56 through 127.94 degrees
360 through 363


92
127.97 through 129.34 degrees
364 through 367


93
129.37 through 130.75 degrees
368 through 371


94
130.78 through 132.16 degrees
372 through 375


95
132.19 through 133.56 degrees
376 through 379


96
133.59 through 134.97 degrees
380 through 383


97
  135 through 136.38 degrees
384 through 387


98
136.41 through 137.78 degrees
388 through 391


99
137.81 through 139.19 degrees
392 through 395


100
139.22 through 140.59 degrees
396 through 399


101
104.62 through 142 degrees
400 through 403


102
142.03 through 143.41 degrees
404 through 407


103
143.44 through 144.81 degrees
408 through 411


104
144.84 through 146.22 degrees
412 through 415


105
146.25 through 147.63 degrees
416 through 419


106
147.66 through 149.03 degrees
420 through 423


107
149.06 through 150.44 degrees
424 through 427


108
150.47 through 151.84 degrees
428 through 431


109
151.87 through 153.25 degrees
432 through 435


110
153.28 through 154.66 degrees
436 through 439


111
154.69 through 156.06 degrees
440 through 443


112
156.09 through 157.47 degrees
444 through 447


113
 157.5 through 158.88 degrees
448 through 451


114
158.91 through 160.28 degrees
452 through 455


115
160.31 through 161.69 degrees
456 through 459


116
161.72 through 163.09 degrees
460 through 463


117
163.12 through 164.5 degrees
464 through 467


118
164.53 through 165.91 degrees
468 through 471


119
165.94 through 167.31 degrees
472 through 475


120
167.34 through 168.72 degrees
476 through 479


121
168.75 through 170.13 degrees
480 through 483


122
170.16 through 171.53 degrees
484 through 487


123
171.56 through 172.94 degrees
488 through 491


124
172.97 through 174.34 degrees
492 through 495


125
174.37 through 175.75 degrees
496 through 499


126
175.78 through 177.16 degrees
500 through 503


127
177.19 through 178.56 degrees
504 through 507


128
178.59 through 179.97 degrees
508 through 511


129
  180 through 181.38 degrees
512 through 515


130
181.41 through 182.78 degrees
516 through 519


131
182.81 through 184.19 degrees
520 through 523


132
184.22 through 185.59 degrees
524 through 527


133
185.62 through 187 degrees
528 through 531


134
187.03 through 188.41 degrees
532 through 535


135
188.44 through 189.81 degrees
536 through 539


136
189.84 through 191.22 degrees
540 through 543


137
191.25 through 192.63 degrees
544 through 547


138
192.66 through 194.03 degrees
548 through 551


139
194.06 through 195.44 degrees
552 through 555


140
195.47 through 196.84 degrees
556 through 559


141
196.87 through 198.25 degrees
560 through 563


142
198.28 through 199.66 degrees
564 through 567


143
199.69 through 201.06 degrees
568 through 571


144
201.09 through 202.47 degrees
572 through 575


145
 202.5 through 203.88 degrees
576 through 579


146
203.91 through 205.28 degrees
580 through 583


147
205.31 through 206.69 degrees
584 through 587


148
206.72 through 208.09 degrees
588 through 591


149
208.12 through 209.5 degrees
592 through 595


150
209.53 through 210.91 degrees
596 through 599


151
210.94 through 212.31 degrees
600 through 603


152
212.34 through 213.72 degrees
604 through 607


153
213.75 through 215.13 degrees
608 through 611


154
215.16 through 216.53 degrees
612 through 615


155
216.56 through 217.94 degrees
616 through 619


156
217.97 through 219.34 degrees
620 through 623


157
219.37 through 220.75 degrees
624 through 627


158
220.78 through 222.16 degrees
628 through 631


159
222.19 through 223.56 degrees
632 through 635


160
223.59 through 224.97 degrees
636 through 639


161
  225 through 226.38 degrees
640 through 643


162
226.41 through 227.78 degrees
644 through 647


163
227.81 through 229.19 degrees
648 through 651


164
229.22 through 230.59 degrees
652 through 655


165
230.62 through 232 degrees
656 through 659


166
232.03 through 233.41 degrees
660 through 663


167
233.44 through 234.81 degrees
664 through 667


168
234.84 through 236.22 degrees
668 through 671


169
236.25 through 237.63 degrees
672 through 675


170
237.66 through 239.03 degrees
676 through 679


171
239.06 through 240.44 degrees
680 through 683


172
240.47 through 241.84 degrees
684 through 687


173
241.88 through 243.25 degrees
688 through 691


174
243.27 through 244.66 degrees
692 through 695


175
244.69 through 246.06 degrees
696 through 699


176
246.09 through 247.47 degrees
700 through 703


177
247.50 through 248.88 degrees
704 through 707


178
248.91 through 250.28 degrees
708 through 711


179
250.31 through 251.69 degrees
712 through 715


180
251.72 through 253.09 degrees
716 through 719


181
253.12 through 254.5 degrees
720 through 723


182
254.53 through 255.91 degrees
724 through 727


183
255.94 through 257.31 degrees
728 through 731


184
257.34 through 258.72 degrees
732 through 735


185
258.75 through 260.13 degrees
736 through 739


186
260.16 through 261.53 degrees
740 through 743


187
261.56 through 262.94 degrees
744 through 747


188
262.97 through 264.34 degrees
748 through 751


189
264.37 through 265.75 degrees
752 through 755


190
265.78 through 267.16 degrees
756 through 759


191
267.19 through 268.56 degrees
760 through 763


192
268.59 through 269.97 degrees
764 through 767


193
  270 through 271.38 degrees
768 through 771


194
271.41 through 272.78 degrees
772 through 775


195
272.81 through 274.19 degrees
776 through 779


196
274.22 through 275.59 degrees
780 through 783


197
275.62 through 277 degrees
784 through 787


198
277.03 through 278.41 degrees
788 through 791


199
278.44 through 279.81 degrees
792 through 795


200
279.84 through 281.22 degrees
796 through 799


201
281.25 through 282.63 degrees
800 through 803


202
282.66 through 284.03 degrees
804 through 807


203
284.06 through 285.44 degrees
808 through 811


204
285.47 through 286.84 degrees
812 through 815


205
286.87 through 288.25 degrees
816 through 819


206
288.28 through 289.66 degrees
820 through 823


207
289.69 through 291.06 degrees
824 through 827


208
291.09 through 292.47 degrees
828 through 831


209
 292.5 through 293.88 degrees
832 through 835


210
293.91 through 295.28 degrees
836 through 839


211
295.31 through 296.69 degrees
840 through 843


212
296.72 through 298.09 degrees
844 through 847


213
298.12 through 299.5 degrees
848 through 851


214
299.53 through 300.91 degrees
852 through 855


215
300.94 through 302.31 degrees
856 through 859


216
302.34 through 303.72 degrees
860 through 863


217
303.75 through 305.13 degrees
864 through 867


218
305.16 through 306.53 degrees
868 through 871


219
306.56 through 307.94 degrees
872 through 875


220
307.97 through 309.34 degrees
876 through 879


221
309.37 through 310.75 degrees
880 through 883


222
310.78 through 312.16 degrees
884 through 887


223
312.19 through 313.56 degrees
888 through 891


224
313.59 through 314.97 degrees
892 through 895


225
  315 through 316.38 degrees
896 through 899


226
316.41 through 317.78 degrees
900 through 903


227
317.81 through 319.19 degrees
904 through 907


228
319.22 through 320.59 degrees
908 through 911


229
320.62 through 322 degrees
912 through 915


230
322.03 through 323.41 degrees
916 through 919


231
323.44 through 324.81 degrees
920 through 923


232
324.84 through 326.22 degrees
924 through 927


233
326.25 through 327.63 degrees
928 through 931


234
327.66 through 329.03 degrees
932 through 935


235
329.06 through 330.44 degrees
936 through 939


236
330.47 through 331.84 degrees
940 through 943


237
331.87 through 333.25 degrees
944 through 947


238
333.28 through 334.66 degrees
948 through 951


239
334.69 through 336.06 degrees
952 through 955


240
336.09 through 337.47 degrees
956 through 959


241
 337.5 through 338.88 degrees
960 through 963


242
338.91 through 340.28 degrees
964 through 967


243
340.31 through 341.69 degrees
968 through 971


244
341.72 through 343.09 degrees
972 through 975


245
343.12 through 344.5 degrees
976 through 979


246
344.53 through 345.91 degrees
980 through 983


247
345.94 through 347.31 degrees
984 through 987


248
347.34 through 348.72 degrees
988 through 991


249
348.75 through 350.13 degrees
992 through 995


250
350.16 through 351.53 degrees
996 through 999


251
351.56 through 352.94 degrees
1000 through 1003


252
352.97 through 354.34 degrees
1004 through 1007


253
354.37 through 355.75 degrees
1008 through 1011


254
355.78 through 357.16 degrees
1012 through 1015


255
357.19 through 358.56 degrees
1016 through 1019


256
358.59 through 359.97 degrees
1020 through 1023
















TABLE 7







512-bit Division









Integer




sent to
logical head location
Heads in Group (2 head


processor
(degrees from center)
grouping = 1 logical head)












0
None
None


1
  0 through .69
0 and 1


2
 0.7 through 1.39
2 and 3


3
1.41 through 2.09
4 and 5


4
2.11 through 2.80
6 and 7


5
2.81 through 3.50
8 and 9


6
3.52 through 4.20
10 and 11


7
4.22 through 4.91
12 and 13


8
4.92 through 5.61
14 and 15


9
5.63 through 6.31
16 and 17


10
6.33 through 7.02
18 and 19


11
7.03 through 7.72
20 and 21


12
7.73 through 8.42
22 and 23


13
8.44 through 9.13
24 and 25


14
9.14 through 9.83
26 and 27


15
 9.84 through 10.53
28 and 29


16
10.55 through 11.23
30 and 31


17
11.25 through 11.94
32 and 33


18
11.95 through 12.64
34 and 35


19
12.66 through 13.34
36 and 37


20
13.36 through 14.05
38 and 39


21
14.06 through 14.75
40 and 41


22
14.77 through 15.45
42 and 43


23
15.47 through 16.16
44 and 45


24
16.17 through 16.86
46 and 47


25
16.87 through 17.56
48 and 49


26
17.58 through 18.27
50 and 51


27
18.28 through 18.97
52 and 53


28
18.98 through 19.67
54 and 55


29
19.69 through 20.38
56 and 57


30
20.39 through 21.08
58 and 59


31
21.09 through 21.78
60 and 61


32
21.80 through 22.48
62 and 63


33
22.50 through 23.19
64 and 65


34
23.20 through 23.89
66 and 67


35
23.91 through 24.59
68 and 69


36
24.61 through 25.30
70 and 71


37
25.31 through 26  
72 and 73


38
26.02 through 26.70
74 and 75


39
26.72 through 27.41
76 and 77


40
27.42 through 28.11
78 and 79


41
28.13 through 28.81
80 and 81


42
28.83 through 29.52
82 and 83


43
29.53 through 30.22
84 and 85


44
30.23 through 30.92
86 and 87


45
30.94 through 31.63
88 and 89


46
31.64 through 32.33
90 and 91


47
32.34 through 33.03
92 and 93


48
33.05 through 33.73
94 and 95


49
33.75 through 34.44
96 and 97


50
34.45 through 35.14
98 and 99


51
35.16 through 35.84
100 and 101


52
35.86 through 36.55
102 and 103


53
36.56 through 37.25
104 and 105


54
37.27 through 37.95
106 and 107


55
37.97 through 38.66
108 and 109


56
38.67 through 39.36
110 and 111


57
39.38 through 40.06
112 and 113


58
40.08 through 40.77
114 and 115


59
40.78 through 41.47
116 and 117


60
41.48 through 42.17
118 and 119


61
42.19 through 42.88
120 and 121


62
42.89 through 43.58
122 and 123


63
43.59 through 44.28
124 and 125


64
44.30 through 44.98
126 and 127


65
  45 through 45.69
128 and 129


66
 45.70 through −46.39
130 and 131


67
46.41 through 47.09
132 and 133


68
47.11 through 47.80
134 and 135


69
47.81 through 48.5 
136 and 137


70
48.52 through 49.20
138 and 139


71
49.22 through 49.91
140 and 141


72
49.92 through 50.61
142 and 143


73
50.63 through 51.31
144 and 145


74
51.33 through 52.02
146 and 147


75
52.03 through 52.72
148 and 149


76
52.73 through 53.42
150 and 151


77
53.44 through 54.13
152 and 153


78
54.14 through 54.83
154 and 155


79
54.84 through 55.53
156 and 157


80
55.55 through 56.23
158 and 159


81
56.25 through 56.94
160 and 161


82
56.95 through 57.64
162 and 163


83
57.66 through 58.34
164 and 165


84
58.36 through 59.05
166 and 167


85
59.06 through 59.75
168 and 169


86
59.77 through 60.45
170 and 171


87
60.47 through 61.16
172 and 173


88
61.17 through 61.86
174 and 175


89
61.88 through 62.56
176 and 177


90
62.58 through 63.27
178 and 179


91
63.28 through 63.97
180 and 181


92
63.98 through 64.67
182 and 183


93
64.69 through 65.38
184 and 185


94
65.39 through 66.08
186 and 187


95
66.09 through 66.78
188 and 189


96
66.80 through 67.48
190 and 191


97
67.50 through 68.19
192 and 193


98
68.20 through 68.89
194 and 195


99
68.91 through 69.59
196 and 197


100
69.61 through 70.30
198 and 199


101
70.31 through 71  
200 and 201


102
71.02 through 71.70
202 and 203


103
71.72 through 72.41
204 and 205


104
72.42 through 73.11
206 and 207


105
73.13 through 73.81
208 and 209


106
73.83 through 74.51
210 and 211


107
74.53 through 75.22
212 and 213


108
75.23 through 75.92
214 and 215


109
75.94 through 76.63
216 and 217


110
76.64 through 77.33
218 and 219


111
77.34 through 78.03
220 and 221


112
78.05 through 78.73
222 and 223


113
78.75 through 79.44
224 and 225


114
79.45 through 80.14
226 and 227


115
80.16 through 80.84
228 and 229


116
80.86 through 81.55
230 and 231


117
81.56 through 82.25
232 and 233


118
82.27 through 82.95
234 and 235


119
82.97 through 83.66
236 and 237


120
83.67 through 84.36
238 and 239


121
84.38 through 85.06
240 and 241


122
85.08 through 85.77
242 and 243


123
85.78 through 86.46
244 and 245


124
86.48 through 87.17
246 and 247


125
87.19 through 87.88
248 and 249


126
87.89 through 88.58
250 and 251


127
88.59 through 89.28
252 and 253


128
89.30 through 89.98
254 and 255


129
  90 through 90.69
256 and 257


130
90.70 through 91.39
258 and 259


131
91.41 through 92.09
260 and 261


132
92.11 through 92.80
262 and 263


133
92.81 through 93.5 
264 and 265


134
93.52 through 94.20
266 and 267


135
94.22 through 94.91
268 and 269


136
94.92 through 95.61
270 and 271


137
95.63 through 96.31
272 and 273


138
96.33 through 97.02
274 and 275


139
97.03 through 97.72
276 and 277


140
97.73 through 98.42
278 and 279


141
98.44 through 99.13
280 and 281


142
99.14 through 99.83
282 and 283


143
 99.84 through 100.53
284 and 285


144
100.55 through 101.23
286 and 287


145
101.25 through 101.94
288 and 289


146
101.95 through 102.64
290 and 291


147
102.66 through 103.34
292 and 293


148
103.36 through 104.05
294 and 295


149
104.06 through 104.75
296 and 297


150
104.77 through 105.45
298 and 299


151
105.47 through 106.16
300 and 301


152
106.17 through 106.86
302 and 303


153
106.88 through 107.56
304 and 305


154
107.58 through 108.27
306 and 307


155
108.28 through 108.97
308 and 309


156
108.98 through 109.67
310 and 311


157
109.69 through 110.38
312 and 313


158
110.39 through 111.08
314 and 315


159
111.09 through 111.78
316 and 317


160
111.80 through 112.48
318 and 319


161
 112.5 through 113.19
320 and 321


162
113.20 through 113.89
322 and 323


163
113.91 through 114.59
324 and 325


164
114.61 through 115.30
326 and 327


165
115.31 through 116  
328 and 329


166
116.01 through 116.70
330 and 331


167
116.72 through 117.41
332 and 333


168
117.42 through 118.11
334 and 335


169
118.13 through 118.81
336 and 337


170
118.83 through 119.52
338 and 339


171
119.53 through 120.22
340 and 341


172
120.23 through 120.92
342 and 343


173
120.94 through 121.63
344 and 345


174
121.64 through 122.33
346 and 347


175
122.34 through 123.03
348 and 349


176
123.05 through 123.73
350 and 351


177
123.75 through 124.44
352 and 353


178
124.45 through 125.14
354 and 355


179
125.16 through 125.84
356 and 357


180
125.86 through 126.54
358 and 359


181
126.56 through 127.25
360 and 361


182
127.27 through 127.95
362 and 363


183
127.97 through 128.66
364 and 365


184
128.67 through 129.36
366 and 367


185
129.38 through 130.06
368 and 369


186
130.08 through 130.77
370 and 371


187
130.78 through 131.47
372 and 373


188
131.48 through 132.17
374 and 375


189
132.19 through 132.88
376 and 377


190
132.89 through 133.58
378 and 379


191
133.59 through 134.28
380 and 381


192
134.30 through 134.98
382 and 383


193
  135 through 135.69
384 and 385


194
135.70 through 136.39
386 and 387


195
136.41 through 137.09
388 and 389


196
137.11 through 137.80
390 and 391


197
137.81 through 138.5 
392 and 393


198
138.52 through 139.20
394 and 395


199
139.22 through 139.91
396 and 397


200
139.92 through 140.61
398 and 399


201
140.63 through 141.31
400 and 401


202
141.33 through 142.02
402 and 403


203
142.03 through 142.72
404 and 405


204
142.73 through 143.42
406 and 407


205
143.44 through 144.13
408 and 409


206
144.14 through 144.83
410 and 411


207
144.84 through 145.53
412 and 413


208
145.55 through 146.23
414 and 415


209
146.25 through 146.94
416 and 417


210
146.95 through 147.64
418 and 419


211
147.66 through 148.34
420 and 421


212
148.36 through 149.05
422 and 423


213
149.06 through 149.75
424 and 425


214
149.77 through 150.45
426 and 427


215
150.47 through 151.16
428 and 429


216
151.17 through 151.86
430 and 431


217
151.88 through 152.56
432 and 433


218
152.58 through 153.27
434 and 435


219
153.28 through 153.97
436 and 437


220
153.98 through 154.67
438 and 439


221
154.69 through 155.38
440 and 441


222
155.39 through 156.08
442 and 443


223
156.09 through 156.78
444 and 445


224
156.80 through 157.48
446 and 447


225
157.50 through 158.19
448 and 449


226
158.20 through 158.89
450 and 451


227
158.91 through 159.59
452 and 453


228
159.61 through 160.30
454 and 455


229
160.31 through 161  
456 and 457


230
161.02 through 161.70
458 and 459


231
161.72 through 162.41
460 and 461


232
162.42 through 163.11
462 and 463


233
163.13 through 163.81
464 and 465


234
163.83 through 164.52
466 and 467


235
164.53 through 165.22
468 and 469


236
165.23 through 165.92
470 and 471


237
165.94 through 166.63
472 and 473


238
166.64 through 167.33
474 and 475


239
167.34 through 168.03
476 and 477


240
168.05 through 168.73
478 and 479


241
168.75 through 169.44
480 and 481


242
169.45 through 170.14
482 and 483


243
170.16 through 170.84
484 and 485


244
170.86 through 171.55
486 and 487


245
171.56 through 172.25
488 and 489


246
172.27 through 172.95
490 and 491


247
172.97 through 173.66
492 and 493


248
173.67 through 174.36
494 and 495


249
174.38 through 175.06
496 and 497


250
175.08 through 175.77
498 and 499


251
175.78 through 176.47
500 and 501


252
176.48 through 177.17
502 and 503


253
177.19 through 177.88
504 and 505


254
177.89 through 178.58
506 and 507


255
178.59 through 179.28
508 and 509


256
179.30 through 179.98
510 and 511


257
  180 through 180.69
512 and 513


258
180.70 through 181.39
514 and 515


259
181.41 through 182.09
516 and 517


260
182.11 through 182.80
518 and 519


261
182.81 through 183.5 
520 and 521


262
183.52 through 184.20
522 and 523


263
184.22 through 184.91
524 and 525


264
184.92 through 185.61
526 and 527


265
185.63 through 186.31
528 and 529


266
186.33 through 187.02
530 and 531


267
187.03 through 187.72
532 and 533


268
187.73 through 188.42
534 and 535


269
188.44 through 189.13
536 and 537


270
189.14 through 189.83
538 and 539


271
189.84 through 190.53
540 and 541


272
190.55 through 191.23
542 and 543


273
191.25 through 191.94
544 and 545


274
191.95 through 192.64
546 and 547


275
192.66 through 193.34
548 and 549


276
193.36 through 194.05
550 and 551


277
194.06 through 194.75
552 and 553


278
194.77 through 195.45
554 and 555


279
195.47 through 196.16
556 and 557


280
196.17 through 196.86
558 and 559


281
196.88 through 197.56
560 and 561


282
197.58 through 198.27
562 and 563


283
198.28 through 198.97
564 and 565


284
198.98 through 199.67
566 and 567


285
199.69 through 200.38
568 and 569


286
200.39 through 201.08
570 and 571


287
201.09 through 201.78
572 and 573


288
201.80 through 202.48
574 and 575


289
 202.5 through 203.19
576 and 577


290
203.20 through 203.89
578 and 579


291
203.91 through 204.59
580 and 581


292
204.61 through 205.30
582 and 583


293
205.31 through 206  
584 and 585


294
206.01 through 206.70
586 and 587


295
206.72 through 207.41
588 and 589


296
207.42 through 208.11
590 and 591


297
208.13 through 208.81
592 and 593


298
208.83 through 209.51
594 and 595


299
209.53 through 210.22
596 and 597


300
210.23 through 210.92
598 and 599


301
210.94 through 211.63
600 and 601


302
211.64 through 212.33
602 and 603


303
212.34 through 213.03
604 and 605


304
213.05 through 213.73
606 and 607


305
213.75 through 214.44
608 and 609


306
214.45 through 215.14
610 and 611


307
215.16 through 215.84
612 and 613


308
215.86 through 216.55
614 and 615


309
216.56 through 217.25
616 and 617


310
217.27 through 217.95
618 and 619


311
217.97 through 218.66
620 and 621


312
218.67 through 219.36
622 and 623


313
219.38 through 220.06
624 and 625


314
220.08 through 220.77
626 and 627


315
220.78 through 221.47
628 and 629


316
221.48 through 222.17
630 and 631


317
222.19 through 222.88
632 and 633


318
222.89 through 223.58
634 and 635


319
223.59 through 224.28
636 and 637


320
224.30 through 224.98
638 and 639


321
  225 through 225.69
640 and 641


322
225.70 through 226.39
642 and 643


323
226.41 through 227.09
644 and 645


324
227.11 through 227.80
646 and 647


325
227.81 through 228.5 
648 and 649


326
228.52 through 229.20
650 and 651


327
229.22 through 229.91
652 and 653


328
229.92 through 230.61
654 and 655


329
230.63 through 231.31
656 and 657


330
231.33 through 232.02
658 and 659


331
232.03 through 232.72
660 and 661


332
232.73 through 233.42
662 and 663


333
233.44 through 234.13
664 and 665


334
234.14 through 234.83
666 and 667


335
234.84 through 235.53
668 and 669


336
235.55 through 236.23
670 and 671


337
236.25 through 236.94
672 and 673


338
236.95 through 237.64
674 and 675


339
237.66 through 238.34
676 and 677


340
238.36 through 239.05
678 and 679


341
239.06 through 239.75
680 and 681


342
239.77 through 240.45
682 and 683


343
240.47 through 241.16
684 and 685


344
241.17 through 241.86
686 and 687


345
241.88-242.56
688 and 689


346
242.58 through 243.27
690 and 691


347
243.28 through 243.97
692 and 693


348
243.98 through 244.67
694 and 695


349
244.69 through 245.38
696 and 697


350
245.39 through 246.08
698 and 699


351
246.09 through 246.78
700 and 701


352
246.80 through 247.48
702 and 703


353
247.50 through 248.19
704 and 705


354
248.20 through 248.89
706 and 707


355
248.91 through 249.59
708 and 709


356
249.61 through 250.30
710 and 711


357
250.31 through 251  
712 and 713


358
251.02 through 251.70
714 and 715


359
251.72 through 252.41
716 and 717


360
252.42 through 253.11
718 and 719


361
253.13 through 253.81
720 and 721


362
253.83 through 254.52
722 and 723


363
254.53 through 255.22
724 and 725


364
255.23 through 255.92
726 and 727


365
255.94 through 256.63
728 and 729


366
256.64 through 257.33
730 and 731


367
257.34 through 258.03
732 and 733


368
258.05 through 258.73
734 and 735


369
258.75 through 259.44
736 and 737


370
259.45 through 260.14
738 and 739


371
260.16 through 260.84
740 and 741


372
260.86 through 261.55
742 and 743


373
261.56 through 262.25
744 and 745


374
262.27 through 262.95
746 and 747


375
262.97 through 263.66
748 and 749


376
263.67 through 264.36
750 and 751


377
264.38 through 265.06
752 and 753


378
265.08 through 265.77
754 and 755


379
265.78 through 266.47
756 and 757


380
266.48 through 267.17
758 and 759


381
267.19 through 267.88
760 and 761


382
267.89 through 268.58
762 and 763


383
268.59 through 269.28
764 and 765


384
269.30 through 269.98
766 and 767


385
  270 through 270.69
768 and 769


386
270.70 through 271.39
770 and 771


387
271.41 through 272.09
772 and 773


388
272.11 through 272.80
774 and 775


389
272.81 through 273.5 
776 and 777


390
273.52 through 274.20
778 and 779


391
274.22 through 274.91
780 and 781


392
274.92 through 275.61
782 and 783


393
275.63 through 276.31
784 and 785


394
276.33 through 277.02
786 and 787


395
277.03 through 277.72
788 and 789


396
277.73 through 278.42
790 and 791


397
278.44 through 279.13
792 and 793


398
279.14 through 279.83
794 and 795


399
279.84 through 280.53
796 and 797


400
280.55 through 281.23
798 and 799


401
281.25 through 281.94
800 and 801


402
281.95 through 282.64
802 and 803


403
282.66 through 283.34
804 and 805


404
283.36 through 284.05
806 and 807


405
284.06 through 284.75
808 and 809


406
284.77 through 285.45
810 and 811


407
285.47 through 286.16
812 and 813


408
286.17 through 286.86
814 and 815


409
286.88 through 287.56
816 and 817


410
287.58 through 288.27
818 and 819


411
288.28 through 288.97
820 and 821


412
288.98 through 289.67
822 and 823


413
289.69 through 290.38
824 and 825


414
290.39 through 291.08
826 and 827


415
291.09 through 291.78
828 and 829


416
291.80 through 292.48
830 and 831


417
 292.5 through 293.19
832 and 833


418
293.20 through 293.89
834 and 835


419
293.91 through 294.59
836 and 837


420
294.61 through 295.30
838 and 839


421
295.31 through 296  
840 and 841


422
296.01 through 296.70
842 and 843


423
296.72 through 297.41
844 and 845


424
297.42 through 298.11
846 and 847


425
298.13 through 298.81
848 and 849


426
298.83 through 299.52
850 and 851


427
299.53 through 300.22
852 and 853


428
300.23 through 300.92
854 and 855


429
300.94 through 301.63
856 and 857


430
301.64 through 302.33
858 and 859


431
302.34 through 303.03
860 and 861


432
303.05 through 303.73
862 and 863


433
303.75 through 304.44
864 and 865


434
304.45 through 305.14
866 and 867


435
305.16 through 305.84
868 and 869


436
305.86 through 306.55
870 and 871


437
306.56 through 307.25
872 and 873


438
307.27 through 307.95
874 and 875


439
307.97 through 308.66
876 and 877


440
308.67 through 309.36
878 and 879


441
309.38 through 310.06
880 and 881


442
310.08 through 310.77
882 and 883


443
310.78 through 311.47
884 and 885


444
311.48 through 312.17
886 and 887


445
312.19 through 312.88
888 and 889


446
312.89 through 313.58
890 and 891


447
313.59 through 314.28
892 and 893


448
314.30 through 314.98
894 and 895


449
  315 through 315.69
896 and 897


450
315.70 through 316.39
898 and 899


451
316.41 through 317.09
900 and 901


452
317.11 through 317.80
902 and 903


453
317.81 through 318.5 
904 and 905


454
318.52 through 319.20
906 and 907


455
319.22 through 319.91
908 and 909


456
319.92 through 320.61
910 and 911


457
320.63 through 321.31
912 and 913


458
321.33 through 322.02
914 and 915


459
322.03 through 322.72
916 and 917


460
322.73 through 323.42
918 and 919


461
323.44 through 324.13
920 and 921


462
324.14 through 324.83
922 and 923


463
324.84 through 325.53
924 and 925


464
325.55 through 326.23
926 and 927


465
326.25 through 326.94
928 and 929


466
326.95 through 327.64
930 and 931


467
327.66 through 328.34
932 and 933


468
328.36 through 329.05
934 and 935


469
329.06 through 329.75
936 and 937


470
329.77 through 330.45
938 and 939


471
330.47 through 331.16
940 and 941


472
331.17 through 331.86
942 and 943


473
331.88 through 332.56
944 and 945


474
332.58 through 333.27
946 and 947


475
333.28 through 333.97
948 and 949


476
333.98 through 334.67
950 and 951


477
334.69 through 335.38
952 and 953


478
335.39 through 336.08
954 and 955


479
336.09 through 336.78
956 and 957


480
336.80 through 337.48
958 and 959


481
 337.5 through 338.19
960 and 961


482
338.20 through 338.89
962 and 963


483
338.91 through 339.59
964 and 965


484
339.61 through 340.30
966 and 967


485
340.31 through 341  
968 and 969


486
341.02 through 341.70
970 and 971


487
341.72 through 342.41
972 and 973


488
342.42 through 343.11
974 and 975


489
343.13 through 343.81
976 and 977


490
343.83 through 344.52
978 and 979


491
344.53 through 345.22
980 and 981


492
345.23 through 345.92
982 and 983


493
345.94 through 346.63
984 and 985


494
346.64 through 347.33
986 and 987


495
347.34 through 348.03
988 and 989


496
348.05 through 348.73
990 and 991


497
348.75 through 349.44
992 and 993


498
349.45 through 350.14
994 and 995


499
350.16 through 350.84
996 and 997


500
350.86 through 351.55
998 and 999


501
351.56 through 352.25
1000 and 1001


502
352.27 through 352.95
1002 and 1003


503
352.97 through 353.66
1004 and 1005


504
353.67 through 354.36
1006 and 1007


505
354.38 through 355.06
1008 and 1009


506
355.08 through 355.77
1010 and 1011


507
355.78 through 356.47
1012 and 1013


508
356.48 through 357.17
1014 and 1015


509
357.19 through 357.88
1016 and 1017


510
357.89 through 358.58
1018 and 1019


511
358.59 through 359.28
1020 and 1021


512
359.30 through 359.98
1022 and 1023
















TABLE 8







1024-bit (1k) Division









Integer sent to
logical head location
Head (one to one physical


processor
(degrees from center)
to logical correlation)












0
None
None


1
0-.344
0


2
.351-.695
1


3
.703-1.047
2


4
1.055-1.398
3


5
1.406-1.750
4


6
1.758-2.102
5


7
2.109-2.453
6


8
2.461-2.805
7


9
2.813-3.156
8


10
3.164-3.508
9


11
3.516-3.859
10


12
3.867-4.211
11


13
4.219-4.563
12


14
4.570-4.914
13


15
4.922-5.266
14


16
5.273-5.617
15


17
5.625-5.969
16


18
5.976-6.320
17


19
6.328-6.672
18


20
6.680-7.023
19


21
7.031-7.375
20


22
7.383-7.727
21


23
7.734-8.078
22


24
8.086-8.430
23


25
8.437-8.781
24


26
8.789-9.133
25


27
9.141-9.484
26


28
9.492-9.836
27


29
9.844-10.188
28


30
10.195-10.539
29


31
10.547-10.891
30


32
10.898-11.242
31


33
11.25-11.594
32


34
11.602-11.945
33


35
11.953-12.297
34


36
12.305-12.648
35


37
12.656-13
36


38
13.008-13.352
37


39
13.359-13.703
38


40
13.711-14.055
39


41
14.063-14.406
40


42
14.414-14.758
41


43
14.766-15.109
42


44
15.117-15.461
43


45
15.469-15.813
44


46
15.820-16.164
45


47
16.172-16.516
46


48
16.523-16.867
47


49
16.875-17.219
48


50
17.227-17.570
49


51
17.578-17.922
50


52
17.930-18.273
51


53
18.281-18.625
52


54
18.633-18.977
53


55
18.984-19.328
54


56
19.336-19.680
55


57
19.688-20.031
56


58
20.039-20.383
57


59
20.391-20.734
58


60
20.742-21.086
59


61
21.093-21.438
60


62
21.445-21.789
61


63
21.797-22.141
62


64
22.148-22.492
63


65
22.5-22.844
64


66
22.852-23.195
65


67
23.203-23.547
66


68
23.555-23.898
67


69
23.906-24.25
68


70
24.258-24.602
69


71
24.609-24.953
70


72
24.961-25.305
71


73
25.313-25.656
72


74
25.664-26.008
73


75
26.016-26.359
74


76
26.367-26.711
75


77
26.719-27.063
76


78
27.070-27.414
77


79
27.422-27.766
78


80
27.773-28.117
79


81
28.125-28.469
80


82
28.477-28.820
81


83
28.828-29.172
82


84
29.180-29.523
83


85
29.531-29.875
84


86
29.883-30.227
85


87
30.234-30.578
86


88
30.586-30.930
87


89
30.938-31.281
88


90
31.289-31.633
89


91
31.641-31.984
90


92
31.992-32.336
91


93
32.344-32.688
92


94
32.695-33.039
93


95
33.047-33.391
94


96
33.398-33.742
95


97
33.75-34.094
96


98
34.102-34.445
97


99
34.453-34.797
98


100
34.805-35.148
99


101
35.156-35.5
100


102
35.508-35.852
101


103
35.859-36.203
102


104
36.211-36.555
103


105
36.563-36.906
104


106
36.914-37.258
105


107
37.266-37.609
106


108
37.617-37.961
107


109
37.969-38.313
108


110
38.320-38.664
109


111
38.672-39.016
110


112
39.023-39.367
111


113
39.375-39.719
112


114
39.727-40.070
113


115
40.078-40.422
114


116
40.430-40.773
115


117
40.781-41.125
116


118
41.133-41.477
117


119
41.484-41.828
118


120
41.836-42.180
119


121
42.188-42.531
120


122
42.539-42.883
121


123
42.891-43.234
122


124
43.242-43.586
123


125
43.594-43.938
124


126
43.945-44.289
125


127
44.297-44.641
126


128
44.648-44.992
127


129
45-45.344
128


130
45.352-45.695
129


131
45.703-46.047
130


132
46.055-46.398
131


133
46.406-46.75
132


134
46.758-47.102
133


135
47.109-47.453
134


136
47.461-47.805
135


137
47.813-48.156
136


138
48.164-48.508
137


139
48.516-48.859
138


140
48.867-49.211
139


141
49.219-49.563
140


142
49.570-49.914
141


143
49.922-50.266
142


144
50.273-50.617
143


145
50.625-50.969
144


146
50.977-51.320
145


147
51.328-51.672
146


148
51.80-52.023
147


149
52.031-52.375
148


150
52.383-52.727
149


151
52.734-53.078
150


152
53.086-53.430
151


153
53.438-53.781
152


154
53.789-54.133
153


155
54.141-54.484
154


156
54.492-54.836
155


157
54.844-55.188
156


158
55.195-55.539
157


159
55.547-55.891
158


160
55.898-56.242
159


161
56.25-56.594
160


162
56.602-56.945
161


163
56.953-57.297
162


164
57.305-57.648
163


165
57.656-58
164


166
58.008-58.352
165


167
58.359-58.703
166


168
58.711-59.055
167


169
59.063-59.406
168


170
59.414-59.758
169


171
59.766-60.109
170


172
60.117-60.461
171


173
60.469-60.813
172


174
60.820-61.164
173


175
61.172-61.516
174


176
61.523-61.867
175


177
61.875-62.219
176


178
62.227-62.570
177


179
62.578-62.922
178


180
62.930-63.273
179


181
63.281-63.625
180


182
63.633-63.977
181


183
63.984-64.328
182


184
64.336-64.680
183


185
64.688-65.031
184


186
65.039-65.383
185


187
65.391-65.734
186


188
65.742-66.086
187


189
66.094-66.438
188


190
66.445-66.789
189


191
66.979-67.141
190


192
67.148-67.492
191


193
67.5-67.844
192


194
67.852-68.195
193


195
68.203-68.547
194


196
68.555-68.898
195


197
68.906-69.25
196


198
69.258-69.602
197


199
69.609-69.953
198


200
69.961-70.305
199


201
70.313-70.656
200


202
70.664-71.008
201


203
71.016-71.359
202


204
71.367-71.711
203


205
71.719-72.063
204


206
72.070-72.414
205


207
72.422-72.766
206


208
72.773-73.117
207


209
73.125-73.469
208


210
73.477-73.820
209


211
73.828-74.172
210


212
74.180-74.523
211


213
74.532-74.875
212


214
74.883-75.226
213


215
75.234-75.578
214


216
75.586-75.930
215


217
75.938-76.281
216


218
76.289-76.633
217


219
76.641-76.984
218


220
76.992-77.336
219


221
77.344-77.688
220


222
77.695-78.039
221


223
78.047-78.391
222


224
78.398-78.742
223


225
78.75-79.094
224


226
79.102-79.445
225


227
79.453-79.797
226


228
79.805-80.148
227


229
80.156-80.5
228


230
80.508-80.852
229


231
80.859-81.203
230


232
81.211-81.555
231


233
81.563-81.906
232


234
81.914-82.258
233


235
82.266-82.609
234


236
82.617-82.961
235


237
82.969-83.313
236


238
83.320-83.664
237


239
83.672-84.016
238


240
84.023-84.367
239


241
84.375-84.719
240


242
84.727-85.070
241


243
85.078-85.422
242


244
85.430-85.773
243


245
85.781-86.125
244


246
86.133-86.477
245


247
86.484-86.828
246


248
86.836-87.180
247


249
87.188-87.531
248


250
87.539-87.883
249


251
87.891-88.234
250


252
88.242-88.586
251


253
88.594-88.938
252


254
88.945-89.289
253


255
89.297-89.641
254


256
89.648-89.992
255


257
90-90.344
256


258
90.352-90.695
257


259
90.703-91.047
258


260
91.055-91.398
259


261
91.406-91.75
260


262
91.758-92.102
261


263
92.109-92.453
262


264
92.461-92.805
263


265
92.813-93.156
264


266
93.164-93.508
265


267
93.516-93.859
266


268
93.867-94.211
267


269
94.219-94.563
268


270
94.570-94.914
269


271
94.922-95.266
270


272
95.273-95.617
271


273
95.625-95.969
272


274
95.977-96.320
273


275
96.328-96.672
274


276
96.680-97.023
275


277
97.031-97.375
276


278
97.383-97.727
277


279
97.734-98.078
278


280
98.086-98.430
279


281
98.438-98.781
280


282
98.789-99.133
281


283
99.141-99.484
282


284
99.492-99.836
283


285
99.844-100.188
284


286
100.195-100.539
285


287
100.547-100.891
286


288
100.898-101.242
287


289
101.25-101.594
288


290
101.602-101.945
289


291
101.953-102.297
290


292
102.305-102.648
291


293
102.656-103
292


294
103.008-103.352
293


295
103.359-103.703
294


296
103.711-104.055
295


297
104.063-104.406
296


298
104.414-104.758
297


299
104.766-105.109
298


300
105.117-105.461
299


301
105.469-105.812
300


302
105.820-106.164
301


303
106.172-106.516
302


304
106.523-106.867
303


305
106.875-107.219
304


306
107.227-107.570
305


307
107.578-107.922
306


308
107.930-108.273
307


309
108.281-108.625
308


310
108.633-108.977
309


311
108.984-109.328
310


312
109.336-109.680
311


313
109.688-110.031
312


314
110.039-110.383
313


315
110.391-110.734
314


316
110.742-111.086
315


317
111.094-111.438
316


318
111.445-111.789
317


319
111.797-112.141
318


320
112.148-112.492
319


321
112.5-112.844
320


322
112.852-113.195
321


323
113.203-113.547
322


324
113.555-113.898
323


325
113.906-114.25
324


326
114.258-114.602
325


327
114.609-114.953
326


328
114.961-115.305
327


329
115.313-115.656
328


330
115.664-116.008
329


331
116.016-116.359
330


332
116.367-116.711
331


333
116.719-117.063
332


334
117.070-117.414
333


335
117.422-117.766
334


336
117.773-118.117
335


337
118.125-118.469
336


338
118.477-118.820
337


339
118.828-119.172
338


340
119.180-119.523
339


341
119.531-119.875
340


342
119.883-120.227
341


343
120.234-120.578
342


344
120.586-120.930
343


345
120.938-121.281
344


346
121.289-121.633
345


347
121.641-121.984
346


348
121.992-122.336
347


349
122.344-122.688
348


350
122.695-123.039
349


351
123.047-123.391
350


352
123.398-123.742
351


353
123.75-124.094
352


354
124.102-124.445
353


355
124.453-124.797
354


356
124.805-125.148
355


357
125.156-125.5
356


358
125.508-125.852
357


359
125.859-126.203
358


360
126.211-126.555
359


361
126.563-126.906
360


362
126.914-127.258
361


363
127.266-127.609
362


364
127.617-127.961
363


365
127.969-128.313
364


366
128.320-128.664
365


367
128.672-129.016
366


368
129.023-129.367
367


369
129.375-129.719
368


370
129.727-130.070
369


371
130.078-130.422
370


372
130.430-130.773
371


373
130.781-131.125
372


374
131.133-131.477
373


375
131.484-131.828
374


376
131.836-132.180
375


377
132.188-132.531
376


378
132.539-132.883
377


379
132.891-133.234
378


380
133.242-133.586
379


381
133.594-133.938
380


382
133.945-134.289
381


383
134.297-134.641
382


384
134.648-134.992
383


385
135-135.344
384


386
135.352-135.695
385


387
135.703-136.047
386


388
136.055-136.398
387


389
136.406-136.75
388


390
136.758-137.102
389


391
137.109-137.453
390


392
137.461-137.805
391


393
137.813-138.157
392


394
138.164-138.508
393


395
138.516-138.859
394


396
138.867-139.211
395


397
139.219-139.563
396


398
139.570-139.914
397


399
139.922-140.266
398


400
140.273-140.617
399


401
140.625-140.969
400


402
140.977-141.320
401


403
141.328-141.672
402


404
141.680-142.023
403


405
142.031-142.375
404


406
142.383-142.727
405


407
142.734-143.078
406


408
143.086-143.430
407


409
143.438-143.781
408


410
143.789-144.133
409


411
144.141-144.484
410


412
144.492-144.836
411


413
144.844-145.188
412


414
145.195-145.539
413


415
145.547-145.891
414


416
145.898-146.242
415


417
146.25-146.594
416


418
146.602-146.945
417


419
146.953-147.297
418


420
147.305-147.648
419


421
147.656-148
420


422
148.008-148.352
421


423
148.359-148.703
422


424
148.711-149.055
423


425
149.063-149.406
424


426
149.414-149.758
425


427
149.766-150.109
426


428
150.117-150.461
427


429
150.469-150.813
428


430
150.820-151.164
429


431
151.172-151.516
430


432
151.523-151.867
431


433
151.875-152.219
432


434
152.227-152.570
433


435
152.578-152.922
434


436
152.930-153.273
435


437
153.281-153.625
436


438
153.633-153.977
437


439
153.984-154.328
438


440
154.336-154.680
439


441
154.688-155.031
440


442
155.039-155.383
441


443
155.391-155.734
442


444
155.742-156.086
443


445
156.094-156.438
444


446
156.445-156.789
445


447
156.797-157.141
446


448
157.148-157.492
447


449
157.5-157.844
448


450
157.852-158.195
449


451
158.203-158.547
450


452
158.555-158.898
451


453
158.906-159.25
452


454
159.258-159.602
453


455
159.609-159.953
454


456
159.961-160.305
455


457
160.313-160.656
456


458
160.664-161.008
457


459
161.016-161.359
458


460
161.367-161.711
459


461
161.719-162.063
460


462
162.070-162.414
461


463
162.422-162.766
462


464
162.773-163.117
463


465
163.125-163.469
464


466
163.477-163.820
465


467
163.828-164.172
466


468
164.180-164.523
467


469
164.531-164.875
468


470
164.883-165.227
469


471
165.234-165.578
470


472
165.586-165.930
471


473
165.938-166.281
472


474
166.289-166.633
473


475
166.641-166.984
474


476
166.992-167.336
475


477
167.344-167.688
476


478
167.695-168.039
477


479
168.047-168.391
478


480
168.398-168.742
479


481
168.75-169.094
480


482
169.102-169.445
481


483
169.453-169.797
482


484
169.805-170.148
483


485
170.156-170.5
484


486
170.508-170.852
485


487
170.859-171.203
486


488
171.211-171.555
487


489
171.563-171.906
488


490
171.914-172.258
489


491
172.266-172.609
490


492
172.617-172.961
491


493
172.969-173.313
492


494
173.320-173.664
493


495
173.672-174.016
494


496
174.023-174.367
495


497
174.375-174.719
496


498
174.727-175.070
497


499
175.078-075.422
498


500
175.430-175.773
499


501
175.781-176.125
500


502
176.133-176.477
501


503
176.484-176.828
502


504
176.836-177.180
503


505
177.188-177.531
504


506
177.539-177.883
505


507
177.891-178.234
506


508
178.242-178.586
507


509
178.594-178.938
508


510
178.945-179.289
509


511
179.297-179.641
510


512
179.648-179.992
511


513
180-180.344
512


514
180.352-180.695
513


515
180.703-181.047
514


516
181.055-181.398
515


517
181.406-181.75
516


518
181.758-182.102
517


519
182.109-182.453
518


520
182.461-182.805
519


521
182.813-183.156
520


522
183.164-183.508
521


523
183.516-183.859
522


524
183.867-184.211
523


525
184.219-184.562
524


526
184.570-184.914
525


527
184.922-185.266
526


528
185.273-185.617
527


529
185.625-185.969
528


530
185.977-186.320
529


531
186.328-186.672
530


532
186.680-187.023
531


533
187.031-187.375
532


534
187.383-187.727
533


535
187.734-188.078
534


536
188.086-188.430
535


537
188.438-188.781
536


538
188.789-189.133
537


539
189.141-189.484
538


540
189.492-189.836
539


541
189.844-190.188
540


542
190.195-190.539
541


543
190.547-190.891
542


544
190.898-191.242
543


545
191.25-191.594
544


546
191.602-191.945
545


547
191.953-192.297
546


548
192.305-192.648
547


549
192.656-193
548


550
193.008-193.352
549


551
193.359-193.703
550


552
193.711-194.055
551


553
194.063-194.406
552


554
194.414-194.758
553


555
194.766-195.109
554


556
195.117-195.461
555


557
195.469-195.813
556


558
195.820-196.164
557


559
196.172-196.516
558


560
196.523-196.867
559


561
196.875-197.219
560


562
197.227-197.570
561


563
197.578-197.922
562


564
197.930-198.273
563


565
198.281-198.625
564


566
198.632-198.977
565


567
198.984-199.328
566


568
199.336-199.680
567


569
199.688-200.031
568


570
200.039-200.383
569


571
200.391-200.734
570


572
200.742-201.086
571


573
201.094-201.438
572


574
201.445-201.789
573


575
201.797-202.141
574


576
202.148-202.492
575


577
202.5-202.844
576


578
202.852-203.195
577


579
203.203-203.547
578


580
203.555-203.898
579


581
203.906-204.25
580


582
204.258-204.602
581


583
204.609-204.953
582


584
204.961-205.305
583


585
205.313-205.656
584


586
205.664-206.008
585


587
206.016-206.359
586


588
206.367-206.711
587


589
206.719-207.063
588


590
207.070-207.414
589


591
207.422-207.766
590


592
207.773-208.117
591


593
208.125-208.469
592


594
208.477-208.820
593


595
208.828-209.172
594


596
209.180-209.523
595


597
209.531-209.875
596


598
209.883-210.227
597


599
210.234-210.578
598


600
210.586-210.930
599


601
210.938-211.281
600


602
211.289-211.633
601


603
211.641-211.984
602


604
211.992-212.336
603


605
212.344-212.688
604


606
212.698-213.039
605


607
213.047-213.391
606


608
213.398-213.742
607


609
213.75-214.094
608


610
214.102-214.445
609


611
214.453-214.797
610


612
214.805-215.148
611


613
215.156-215.5
612


614
215.508-215.852
613


615
215.859-216.203
614


616
216.211-216.555
615


617
216.563-216.906
616


618
216.914-217.258
617


619
217.266-217.609
618


620
217.617-217.961
619


621
217.969-218.313
620


622
218.320-218.664
621


623
218.672-219.016
622


624
219.023-219.367
623


625
219.375-219.719
624


626
219.727-220.070
625


627
220.078-220.422
626


628
220.430-220.773
627


629
220.781-221.125
628


630
221.133-221.477
629


631
221.484-221.828
630


632
221.836-222.180
631


633
222.188-222.531
632


634
222.539-222.883
633


635
222.891-223.234
634


636
223.242-223.586
635


637
223.594-223.938
636


638
223.945-224.289
637


639
224.297-224.641
638


640
224.648-224.992
639


641
225-225.344
640


642
225.352-225.695
641


643
225.703-226.047
642


644
226.055-226.398
643


645
226.406-226.75
644


646
226.758-227.102
645


647
227.109-227.453
646


648
227.461-227.805
647


649
227.813-228.156
648


650
228.164-228.508
649


651
228.516-228.859
650


652
228.867-229.211
651


653
229.219-229.563
652


654
229.570-229.914
653


655
229.922-230.266
654


656
230.273-230.617
655


657
230.625-230.969
656


658
230.977-231.320
657


659
231.328-231.672
658


660
231.680-232.023
659


661
232.031-232.375
660


662
232.383-232.727
661


663
232.734-233.078
662


664
233.086-233.430
663


665
233.438-233.781
664


666
233.789-234.133
665


667
234.141-234.484
666


668
234.492-234.836
667


669
234.844-235.188
668


670
235.195-235.539
669


671
235.547-235.891
670


672
235.898-236.242
671


673
236.25-236.594
672


674
236.602-236.945
673


675
236.953-237.297
674


676
237.305-237.648
675


677
237.656-238
676


678
238.008-238.352
677


679
238.359-238.703
678


680
238.711-239.055
679


681
239.063-239.406
680


682
239.414-239.758
681


683
239.766-240.109
682


684
240.117-240.461
683


685
240.469-240.813
684


686
240.820-241.164
685


687
241.172-241.516
686


688
241.523-241.867
687


689
241.875-242.219
688


690
242.227-242.570
689


691
242.578-242.922
690


692
242.930-243.273
691


693
243.281-243.625
692


694
243.633-243.977
693


695
243.984-244.328
694


696
244.336-244.680
695


697
244.688-245.031
696


698
245.039-245.383
697


699
245.391-245.734
698


700
245.742-246.086
699


701
246.094-246.438
700


702
246.445-246.789
701


703
246.797-247.141
702


704
247.148-247.492
703


705
247.5-247.844
704


706
247.852-248.195
705


707
248.203-248.547
706


708
248.555-248.898
707


709
248.906-249.25
708


710
249.258-249.602
709


711
249.609-249.953
710


712
249.961-250.305
711


713
250.313-250.656
712


714
250.664-251.008
713


715
251.016-251.359
714


716
251.367-251.711
715


717
251.719-252.063
716


718
252.070-252.414
717


719
252.422-252.766
718


720
252.773-253.117
719


721
253.125-253.469
720


722
253.477-253.820
721


723
253.828-254.172
722


724
254.180-254.523
723


725
254.531-254.875
724


726
254.883-255.227
725


727
255.234-255.578
726


728
255.586-255.930
727


729
255.938-256.281
728


730
256.289-256.633
729


731
256.641-256.984
730


732
256.992-257.336
731


733
257.344-257.688
732


734
257.695-258.039
733


735
258.047-258.391
734


736
258.398-258.742
735


737
258.75-259.094
736


738
259.102-259.445
737


739
259.453-259.797
738


740
259.805-260.148
739


741
260.156-260.5
740


742
260.508-260.852
741


743
260.859-261.203
742


744
261.211-261.555
743


745
261.563-261.906
744


746
261.914-262.258
745


747
262.266-262.609
746


748
262.617-262.961
747


749
262.969-263.313
748


750
263.320-263.664
749


751
263.672-264.016
750


752
264.023-264.367
751


753
264.375-264.719
752


754
264.727-265.070
753


755
265.078-265.422
754


756
265.430-265.773
755


757
265.781-266.125
756


758
266.133-266.477
757


759
266.484-266.828
758


760
266.836-267.180
759


761
267.188-267.531
760


762
267.539-267.883
761


763
267.891-268.234
762


764
268.242-268.586
763


765
268.594-268.938
764


766
268.945-269.289
765


767
269.297-269.641
766


768
269.648-269.992
767


769
270-270.344
768


770
270.352-270.695
769


771
270.703-271.047
770


772
271.055-271.398
771


773
271.406-271.75
772


774
271.758-272.102
773


775
272.109-272.453
774


776
272.461-272.805
775


777
272.813-273.156
776


778
273.164-273.508
777


779
273.516-273.859
778


780
273.867-274.211
779


781
274.219-274.563
780


782
274.570-274.914
781


783
274.922-275.266
782


784
275.273-275.617
783


785
275.625-275.969
784


786
275.977-276.320
785


787
276.328-276.672
786


788
276.680-277.023
787


789
277.031-277.375
788


790
277.383-277.727
789


791
277.734-278.078
790


792
278.086-278.430
791


793
278.438-278.781
792


794
278.789-279.133
793


795
279.141-279.484
794


796
279.492-279.836
795


797
279.844-280.188
796


798
280.195-280.539
797


799
280.547-280.891
798


800
280.898-281.242
799


801
281.25-281.594
800


802
281.602-281.945
801


803
281.953-282.297
802


814
282.305-282.648
803


805
282.656-283
814


806
283.008-283.352
805


807
283.359-283.703
806


808
283.711-284.055
807


809
284.063-284.406
808


810
284.414-284.758
809


811
284.766-285.109
810


812
285.117-285.461
811


813
285.469-285.813
812


814
285.820-286.164
813


815
286.172-286.516
814


816
286.523-286.867
815


817
286.875-287.219
816


818
287.227-287.570
817


819
287.578-287.922
818


820
287.930-288.273
819


821
288.281-288.625
820


822
288.633-288.977
821


823
288.984-289.328
822


824
289.336-289.680
823


825
289.688-290.031
824


826
290.039-290.383
825


827
290.391-290.734
826


828
290.742-291.086
827


829
291.094-291.438
828


830
291.445-291.789
829


831
291.797-292.141
830


832
292.148-292.492
831


833
292.5-292.844
832


834
292.852-293.195
833


835
293.203-293.547
834


836
293.555-293.898
835


837
293.906-294.25
836


838
294.258-294.602
837


839
294.609-294.953
838


840
294.691-295.305
839


841
295.313-295.656
840


842
295.664-296.008
841


843
296.016-296.359
842


844
296.367-296.711
843


845
296.719-297.063
844


846
297.070-297.414
845


847
297.422-297.766
846


848
297.773-298.117
847


849
298.125-298.469
848


850
298.477-298.820
849


851
298.828-299.172
850


852
299.180-299.523
851


853
299.531-299.875
852


854
299.883-300.227
853


855
300.234-300.578
854


856
300.586-300.930
855


857
300.938-301.281
856


858
301.289-301.633
857


859
301.641-301.984
858


860
301.992-302.336
859


861
302.344-302.688
860


862
302.695-303.039
861


863
303.047-303.391
862


864
303.398-303.742
863


865
303.75-304.094
864


866
304.102-304.445
865


867
304.453-304.797
866


868
304.805-305.148
867


869
305.156-305.5
868


870
305.508-305.852
869


871
305.859-306.203
870


872
306.211-306.555
871


873
306.563-306.906
872


874
306.914-307.258
873


875
307.266-307.609
874


876
307.617-307.961
875


877
307.969-308.313
876


878
308.320-308.664
877


879
308.672-309.016
878


880
309.023-309.367
879


881
309.375-309.719
880


882
309.727-310.070
881


883
310.078-310.422
882


884
310.430-310.773
883


885
310.781-311.125
884


886
311.133-311.477
885


887
311.484-311.828
886


888
311.836-312.180
887


889
312.188-312.531
888


890
312.539-312.883
889


891
312.891-313.234
890


892
313.242-313.586
891


893
313.594-313.938
892


894
313.945-314.289
893


895
314.297-314.641
894


896
314.648-314.992
895


897
315-315.344
896


898
315.352-315.695
897


899
315.703-316.047
898


900
316.055-316.398
899


901
316.406-316.75
900


902
316.758-317.102
901


903
317.109-317.453
902


904
317.461-317.805
903


905
317.813-318.156
904


906
318.164-318.508
905


907
318.516-318.859
906


908
318.867-319.211
907


909
319.219-319.563
908


910
319.570-319.914
909


911
319.922-320.266
910


912
320.273-320.617
911


913
320.625-320.969
912


914
320.977-321.320
913


915
321.328-321.672
914


916
321.680-322.023
915


917
322.031-322.375
916


918
322.383-322.727
917


919
322.734-323.078
918


920
323.086-323.430
919


921
323.438-323.781
920


922
323.789-324.133
921


923
324.141-324.484
922


924
324.492-324.836
923


925
324.844-325.188
924


926
325.195-325.539
925


927
325.547-325.891
926


928
325.898-326.242
927


929
326.25-326.594
928


930
326.602-326.945
929


931
326.953-327.297
930


932
327.305-327.648
931


933
327.656-328
932


934
328.008-328.352
933


935
328.359-328.703
934


936
328.711-329.055
935


937
329.063-329.406
936


938
329.414-329.758
937


939
329.766-330.109
938


940
330.117-330.461
939


941
330.469-330.813
940


942
330.820-331.164
941


943
331.172-331.516
942


944
331.523-331.867
943


945
331.875-332.219
944


946
332.227-332.570
945


947
332.578-332.922
946


948
332.930-333.273
947


949
333.281-333.625
948


950
333.633-333.977
949


951
333.984-334.328
950


952
334.336-334.680
951


953
334.688-335.031
952


954
335.039-335.383
953


955
335.391-335.734
954


956
335.742-336.086
955


957
336.094-336.438
956


958
336.445-336.789
957


959
336.797-337.141
958


960
337.148-337.492
959


961
337.5-337.844
960


962
337.852-338.195
961


963
338.203-338.547
962


964
338.555-338.898
963


965
338.906-339.25
964


966
339.258-339.602
965


967
339.609-339.953
966


968
339.961-340.305
967


969
340.313-340.656
968


970
340.664-341.008
969


971
341.016-341.359
970


972
341.367-341.711
971


973
341.719-342.063
972


974
342.070-342.414
973


975
342.422-342.766
974


976
342.773-343.117
975


977
343.125-343.469
976


978
343.477-343.820
977


979
343.828-344.172
978


980
344.180-344.523
979


981
344.531-344.875
980


982
344.883-345.227
981


983
345.234-345.578
982


984
345.586-345.930
983


985
345.938-346.281
984


986
346.289-346.633
985


987
346.641-346.984
986


988
346.992-347.336
987


989
347.344-347.688
988


990
347.695-348.039
989


991
348.047-348.391
990


992
348.398-348.742
991


993
348.75-349.094
992


994
349.102-349.445
993


995
349.453-349.797
994


996
349.805-350.148
995


997
350.156-350.5
996


998
350.508-350.852
997


999
350.859-351.203
998


1000
351.211-351.555
999


1001
351.563-351.906
1000


1002
351.914-352.258
1001


1003
352.266-352.609
1002


1004
352.617-352.961
1003


1005
352.969-353.313
1004


1006
353.320-353.664
1005


1007
353.672-354.016
1006


1008
354.023-354.367
1007


1009
354.375-354.719
1008


1010
354.727-355.070
1009


1011
355.078-355.422
1010


1012
355.430-355.773
1011


1013
355.781-356.125
1012


1014
356.133-356.477
1013


1015
356.484-356.828
1014


1016
356.836-357.180
1015


1017
357.188-357.531
1016


1018
357.539-357.883
1017


1019
357.891-358.234
1018


1020
358.242-358.586
1019


1021
358.594-358.938
1020


1022
358.945-359.289
1021


1023
359.297-359.641
1022


1024
359.648-359.992
1023

## Claims

1. An optical disc containing information units arranged spirally from the disc center to the outer radial edge of the disc which are uniform in shape and size, with each unit containing a reflective pad which is raised from the disc surface, rather than sunken into the disc as a pit, designed to reflect incident light away from the surface of the disc in the shape of a straight line at an angle of 45 degrees from the disc surface and at one of 1024 preset angles between 0 degrees and 360 degrees from the center of the light source with 0 degrees oriented radially towards the center of the disc.

2. An optical apparatus for reproducing data from the disc noted in claim 1, comprised of:
a laser light source that moves in a radial path along the underside of the optical disc as the disc spins in a circumferential direction, and which laser light source irradiates the raised pads in the informational units on the surface of the optical disc to produce reflections in one of 1024 preset angles;
a laser light detecting ring comprised of 210 individual light detecting receptors arranged circumferentially around the laser light source and also attached to the laser light source so as to move with said source, remaining at a constant distance from both the light source and the disc surface as the light source moves in its radial path allowing the laser light receptors in the ring to be irradiated as light is reflected from the raised pads in the informational units on the disc; and
a processor capable of determining which receptor is irradiated by the reflected light from each information unit, and outputting a data value between 1 and 1024 accordingly.

3. An apparatus according to claim 2, where 2 10/x (where x is an integer whose value is 128, 64, 32, 16, 8, 4, or 2) contiguous receptors in the laser light detecting ring are interpreted by the processor as being a single, logical receptor thereby dynamically combining adjacent receptors to form 8, 16, 32, 64, 128, 256, or 512 logical receptors from the 1024 physical receptors so that when any light detecting receptor of a contiguous group is irradiated by reflected light, the output from the processor is the same.