Cylinder-head-sector ( CHS ) is an early method for giving addresses to each physical block of data on a hard disk drive .
71-432: It is a 3D-coordinate system made out of a vertical coordinate head , a horizontal (or radial) coordinate cylinder , and an angular coordinate sector . Head selects a circular surface: a platter in the disk (and one of its two sides). Cylinder is a cylindrical intersection through the stack of platters in a disk, centered around the disk's spindle. Combined, cylinder and head intersect to a circular line, or more precisely:
142-454: A = r sin α . {\displaystyle {\begin{aligned}e&=\cos \alpha ,\\[1ex]a&={\frac {r}{\sin \alpha }}.\end{aligned}}} If the base of a circular cylinder has a radius r and the cylinder has height h , then its volume is given by V = π r 2 h {\displaystyle V=\pi r^{2}h} This formula holds whether or not
213-456: A d s + h ) × N s e c t o r s + ( s − 1 ) , {\displaystyle A=(c\times N_{\mathrm {heads} }+h)\times N_{\mathrm {sectors} }+(s-1),} where A is the LBA address, N heads is the number of heads on the disk, N sectors is the maximum number of sectors per track, and ( c , h , s )
284-406: A CKD disk . The concept is concentric, through the physical platters , being a data circle per each cylinder of the whole disk drive. In other words, the number of tracks on a single surface in the drive exactly equals the number of cylinders of the drive. Tracks are subdivided into blocks (or sectors, pages) (see: Storage block and Virtual page ). The term track is sometimes prefaced with
355-410: A track , where the track is determined by the head and cylinder numbers. The terms are explained bottom up, for disk addressing the sector is the smallest unit. Disk controllers can introduce address translations to map logical to physical positions, e.g., zone bit recording stores fewer sectors in shorter (inner) tracks, physical disk formats are not necessarily cylindrical, and sector numbers in
426-497: A circular strip of physical data blocks called track . Sector finally selects which data block in this track is to be addressed, as the track is subdivided into several equally-sized portions, each of which is an arc of (360/n) degrees, where n is the number of sectors in the track. CHS addresses were exposed, instead of simple linear addresses (going from 0 to the total block count on disk - 1 ), because early hard drives didn't come with an embedded disk controller , that would hide
497-425: A common integration technique for finding volumes of solids of revolution. In the treatise by this name, written c. 225 BCE , Archimedes obtained the result of which he was most proud, namely obtaining the formulas for the volume and surface area of a sphere by exploiting the relationship between a sphere and its circumscribed right circular cylinder of the same height and diameter . The sphere has
568-468: A disk. The Unix communities employ the term block to refer to a sector or group of sectors. For example, the Linux fdisk utility, before version 2.25, displayed partition sizes using 1024-byte blocks . Clusters are allocation units for data on various file systems ( FAT , NTFS , etc.), where data mainly consists of files. Clusters are not directly affected by the physical or virtual geometry of
639-407: A height much greater than its diameter, whereas a short and wide disk cylinder has a diameter much greater than its height. A cylindric section is the intersection of a cylinder's surface with a plane . They are, in general, curves and are special types of plane sections . The cylindric section by a plane that contains two elements of a cylinder is a parallelogram . Such a cylindric section of
710-410: A plane intersects a base of the cylinder in exactly two points then the line segment joining these points is part of the cylindric section. If such a plane contains two elements, it has a rectangle as a cylindric section, otherwise the sides of the cylindric section are portions of an ellipse. Finally, if a plane contains more than two points of a base, it contains the entire base and the cylindric section
781-407: A plane not parallel to the given line. Such cylinders have, at times, been referred to as generalized cylinders . Through each point of a generalized cylinder there passes a unique line that is contained in the cylinder. Thus, this definition may be rephrased to say that a cylinder is any ruled surface spanned by a one-parameter family of parallel lines. A cylinder having a right section that
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#1732776827712852-507: A polyhedral viewpoint, a cylinder can also be seen as a dual of a bicone as an infinite-sided bipyramid . Track (disk drive) A disk drive track is a circular path on the surface of a disk or diskette on which information is magnetically recorded and from which recorded information is read. A track is a physical division of data in a disk drive, as used in the Cylinder-Head-Record (CCHHR) addressing mode of
923-407: A right cylinder is a rectangle . A cylindric section in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a right section . If a right section of a cylinder is a circle then the cylinder is a circular cylinder. In more generality, if a right section of a cylinder is a conic section (parabola, ellipse, hyperbola) then the solid cylinder
994-399: A right cylinder, is more generally given by L = e × p , {\displaystyle L=e\times p,} where e is the length of an element and p is the perimeter of a right section of the cylinder. This produces the previous formula for lateral area when the cylinder is a right circular cylinder. A right circular hollow cylinder (or cylindrical shell )
1065-510: A roughly 128 GB limit; actually 65536×16×255=267386880 sectors corresponding to 130560 MB for a sector size of 512 bytes. The 28=16+4+8 bits in the ATA-2 specification are also covered by Ralf Brown's Interrupt List , and an old working draft of this now expired standard was published. With an old BIOS limit of 1024 cylinders and the ATA limit of 16 heads the combined effect
1136-409: A single real line (actually a coincident pair of lines), or only at the vertex. These cases give rise to the hyperbolic, parabolic or elliptic cylinders respectively. This concept is useful when considering degenerate conics , which may include the cylindrical conics. A solid circular cylinder can be seen as the limiting case of a n -gonal prism where n approaches infinity . The connection
1207-542: A single real point.) If A and B have different signs and ρ ≠ 0 {\displaystyle \rho \neq 0} , we obtain the hyperbolic cylinders , whose equations may be rewritten as: ( x a ) 2 − ( y b ) 2 = 1. {\displaystyle \left({\frac {x}{a}}\right)^{2}-\left({\frac {y}{b}}\right)^{2}=1.} Finally, if AB = 0 assume, without loss of generality , that B = 0 and A = 1 to obtain
1278-612: A track can be skewed. Floppy disks and controllers had used physical sector sizes of 128, 256, 512 and 1024 bytes (e.g., PC/AX), but formats with 512 bytes per physical sector became dominant in the 1980s. The most common physical sector size for hard disks today is 512 bytes, but there have been hard disks with 520 bytes per sector as well for non-IBM compatible machines. In 2005 some Seagate custom hard disks used sector sizes of 1024 bytes per sector. Advanced Format hard disks use 4096 bytes per physical sector ( 4Kn ) since 2010, but will also be able to emulate 512 byte sectors ( 512e ) for
1349-503: A transitional period. Magneto-optical drives use sector sizes of 512 and 1024 bytes on 5.25-inch drives and 512 and 2048 bytes on 3.5-inch drives. In CHS addressing the sector numbers always start at 1 , there is no sector 0 , which can lead to confusion since logical sector addressing schemes typically start counting with 0, e.g., logical block addressing (LBA), or "relative sector addressing" used in DOS. For physical disk geometries
1420-411: A volume two-thirds that of the circumscribed cylinder and a surface area two-thirds that of the cylinder (including the bases). Since the values for the cylinder were already known, he obtained, for the first time, the corresponding values for the sphere. The volume of a sphere of radius r is 4 / 3 π r = 2 / 3 (2 π r ) . The surface area of this sphere
1491-421: Is 4 π r = 2 / 3 (6 π r ) . A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request. In some areas of geometry and topology the term cylinder refers to what has been called a cylindrical surface . A cylinder is defined as a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in
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#17327768277121562-403: Is a circle. In the case of a right circular cylinder with a cylindric section that is an ellipse, the eccentricity e of the cylindric section and semi-major axis a of the cylindric section depend on the radius of the cylinder r and the angle α between the secant plane and cylinder axis, in the following way: e = cos α ,
1633-465: Is a division of data in a disk drive , as used in the CHS addressing mode of a Fixed Block Architecture disk or the cylinder–head–record (CCHHR) addressing mode of a CKD disk . The concept is concentric, hollow, cylindrical slices through the physical disks ( platters ), collecting the respective circular tracks aligned through the stack of platters. The number of cylinders of a disk drive exactly equals
1704-761: Is a generalization of the equation of the ordinary, circular cylinder ( a = b ). Elliptic cylinders are also known as cylindroids , but that name is ambiguous, as it can also refer to the Plücker conoid . If ρ {\displaystyle \rho } has a different sign than the coefficients, we obtain the imaginary elliptic cylinders : ( x a ) 2 + ( y b ) 2 = − 1 , {\displaystyle \left({\frac {x}{a}}\right)^{2}+\left({\frac {y}{b}}\right)^{2}=-1,} which have no real points on them. ( ρ = 0 {\displaystyle \rho =0} gives
1775-405: Is a right circular cylinder. The height of a cylinder of revolution is the length of the generating line segment. The line that the segment is revolved about is called the axis of the cylinder and it passes through the centers of the two bases. The bare term cylinder often refers to a solid cylinder with circular ends perpendicular to the axis, that is, a right circular cylinder, as shown in
1846-613: Is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel annular bases perpendicular to the cylinders' common axis, as in the diagram. Let the height be h , internal radius r , and external radius R . The volume is given by V = π ( R 2 − r 2 ) h = 2 π ( R + r 2 ) h ( R − r ) . {\displaystyle V=\pi \left(R^{2}-r^{2}\right)h=2\pi \left({\frac {R+r}{2}}\right)h(R-r).} Thus,
1917-638: Is an ellipse , parabola , or hyperbola is called an elliptic cylinder , parabolic cylinder and hyperbolic cylinder , respectively. These are degenerate quadric surfaces . When the principal axes of a quadric are aligned with the reference frame (always possible for a quadric), a general equation of the quadric in three dimensions is given by f ( x , y , z ) = A x 2 + B y 2 + C z 2 + D x + E y + G z + H = 0 , {\displaystyle f(x,y,z)=Ax^{2}+By^{2}+Cz^{2}+Dx+Ey+Gz+H=0,} with
1988-426: Is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology . The shift in the basic meaning—solid versus surface (as in a solid ball versus sphere surface)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces . In
2059-416: Is required to read a single track. With respect to disk geometries the terms track and cylinder are closely related. For a single or double sided floppy disk track is the common term; and for more than two heads cylinder is the common term. Strictly speaking a track is a given C H combination consisting of SPT sectors, while a cylinder consists of SPT× H sectors. A cylinder
2130-403: Is said to be parabolic, elliptic and hyperbolic, respectively. For a right circular cylinder, there are several ways in which planes can meet a cylinder. First, planes that intersect a base in at most one point. A plane is tangent to the cylinder if it meets the cylinder in a single element. The right sections are circles and all other planes intersect the cylindrical surface in an ellipse . If
2201-425: Is the diameter of the circular top or bottom. For a given volume, the right circular cylinder with the smallest surface area has h = 2 r . Equivalently, for a given surface area, the right circular cylinder with the largest volume has h = 2 r , that is, the cylinder fits snugly in a cube of side length = altitude ( = diameter of base circle). The lateral area, L , of a circular cylinder, which need not be
Cylinder-head-sector - Misplaced Pages Continue
2272-459: Is the CHS address. A Logical Sector Number formula in the ECMA -107 and ISO / IEC 9293:1994 (superseding ISO 9293:1987) standards for FAT file systems matches exactly the LBA formula given above: Logical Block Address and Logical Sector Number (LSN) are synonyms. The formula does not use the number of cylinders, but requires the number of heads and the number of sectors per track in
2343-641: Is the equation of an elliptic cylinder . Further simplification can be obtained by translation of axes and scalar multiplication. If ρ {\displaystyle \rho } has the same sign as the coefficients A and B , then the equation of an elliptic cylinder may be rewritten in Cartesian coordinates as: ( x a ) 2 + ( y b ) 2 = 1. {\displaystyle \left({\frac {x}{a}}\right)^{2}+\left({\frac {y}{b}}\right)^{2}=1.} This equation of an elliptic cylinder
2414-484: Is the first (outer-most) track on floppy or other cylindrical disks. Old BIOS code supported ten bits in CHS addressing with up to 1024 cylinders ( 1024=2 ). Adding six bits for sectors and eight bits for heads results in the 24 bits supported by BIOS interrupt 13h . Subtracting the disallowed sector number 0 in 1024×256 tracks corresponds to 128 MB for a sector size of 512 bytes ( 128 MB =1024×256×(512 byte/sector) ); and 8192-128=8064 confirms
2485-426: Is the only type of geometric figure for which this technique works with the use of only elementary considerations (no appeal to calculus or more advanced mathematics). Terminology about prisms and cylinders is identical. Thus, for example, since a truncated prism is a prism whose bases do not lie in parallel planes, a solid cylinder whose bases do not lie in parallel planes would be called a truncated cylinder . From
2556-407: Is very strong and many older texts treat prisms and cylinders simultaneously. Formulas for surface area and volume are derived from the corresponding formulas for prisms by using inscribed and circumscribed prisms and then letting the number of sides of the prism increase without bound. One reason for the early emphasis (and sometimes exclusive treatment) on circular cylinders is that a circular base
2627-535: The IBM 2321 Data Cell , might give blocks addresses that include a cylinder address, although the cylinder address doesn't select a (geometric) cylindrical slice of the device. A device called a head reads and writes data in a hard drive by manipulating the magnetic medium that composes the surface of an associated disk platter. Naturally, a platter has 2 sides and thus 2 surfaces on which data can be manipulated; usually there are 2 heads per platter, one per side. (Sometimes
2698-409: The parabolic cylinders with equations that can be written as: x 2 + 2 a y = 0. {\displaystyle x^{2}+2ay=0.} In projective geometry , a cylinder is simply a cone whose apex (vertex) lies on the plane at infinity . If the cone is a quadratic cone, the plane at infinity (which passes through the vertex) can intersect the cone at two real lines,
2769-489: The surface area of a right circular cylinder, oriented so that its axis is vertical, consists of three parts: The area of the top and bottom bases is the same, and is called the base area , B . The area of the side is known as the lateral area , L . An open cylinder does not include either top or bottom elements, and therefore has surface area (lateral area) L = 2 π r h {\displaystyle L=2\pi rh} The surface area of
2840-452: The (roughly) 8 GB limit. CHS addressing starts at 0/0/1 with a maximal value 1023/255/63 for 24=10+8+6 bits, or 1023/254/63 for 24 bits limited to 255 heads . CHS values used to specify the geometry of a disk have to count cylinder 0 and head 0 resulting in a maximum ( 1024/256/63 or) 1024/255/63 for 24 bits with (256 or) 255 heads. In CHS tuples specifying a geometry S actually means sectors per track, and where
2911-446: The (virtual) geometry still matches the capacity the disk contains C×H×S sectors. As larger hard disks have come into use, a cylinder has become also a logical disk structure, standardised at 16 065 sectors ( 16065=255×63 ). CHS addressing with 28 bits ( EIDE and ATA-2 ) permits eight bits for sectors still starting at 1, i.e., sectors 1...255, four bits for heads 0...15, and sixteen bits for cylinders 0...65535. This results in
Cylinder-head-sector - Misplaced Pages Continue
2982-422: The CHS values matched the physical properties of the drive. A drive with a CHS tuple of 500 4 32 would have 500 tracks per side on each platter, two platters (4 heads), and 32 sectors per track, with a total of 32 768 000 bytes (31.25 MiB ). ATA/IDE drives were much more efficient at storing data and have replaced the now-obsolete MFM and RLL drives. They use zone bit recording (ZBR), where
3053-533: The axis of the cylinder is taken as the positive x -axis and A ( x ) = A the area of each elliptic cross-section, thus: V = ∫ 0 h A ( x ) d x = ∫ 0 h π a b d x = π a b ∫ 0 h d x = π a b h . {\displaystyle V=\int _{0}^{h}A(x)dx=\int _{0}^{h}\pi abdx=\pi ab\int _{0}^{h}dx=\pi abh.} Using cylindrical coordinates ,
3124-440: The bases are disks (regions whose boundary is a circle ) the cylinder is called a circular cylinder . In some elementary treatments, a cylinder always means a circular cylinder. The height (or altitude) of a cylinder is the perpendicular distance between its bases. The cylinder obtained by rotating a line segment about a fixed line that it is parallel to is a cylinder of revolution . A cylinder of revolution
3195-904: The coefficients being real numbers and not all of A , B and C being 0. If at least one variable does not appear in the equation, then the quadric is degenerate. If one variable is missing, we may assume by an appropriate rotation of axes that the variable z does not appear and the general equation of this type of degenerate quadric can be written as A ( x + D 2 A ) 2 + B ( y + E 2 B ) 2 = ρ , {\displaystyle A\left(x+{\frac {D}{2A}}\right)^{2}+B\left(y+{\frac {E}{2B}}\right)^{2}=\rho ,} where ρ = − H + D 2 4 A + E 2 4 B . {\displaystyle \rho =-H+{\frac {D^{2}}{4A}}+{\frac {E^{2}}{4B}}.} If AB > 0 this
3266-410: The controller, thus CHS addressing no longer corresponded to any physical attributes of the drive. By the mid 1990s, hard drive interfaces replaced the CHS scheme with logical block addressing (LBA), but many tools for manipulating the master boot record (MBR) partition table still aligned partitions to cylinder boundaries; thus, artifacts of CHS addressing were still seen in partitioning software by
3337-416: The cylinder . All the elements of a cylinder have equal lengths. The region bounded by the cylindrical surface in either of the parallel planes is called a base of the cylinder. The two bases of a cylinder are congruent figures. If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder , otherwise it is called an oblique cylinder . If
3408-505: The cylinder is a right cylinder. This formula may be established by using Cavalieri's principle . In more generality, by the same principle, the volume of any cylinder is the product of the area of a base and the height. For example, an elliptic cylinder with a base having semi-major axis a , semi-minor axis b and height h has a volume V = Ah , where A is the area of the base ellipse (= π ab ). This result for right elliptic cylinders can also be obtained by integration, where
3479-492: The disk geometry, because the same CHS tuple addresses different logical sector numbers depending on the geometry. Examples : To help visualize the sequencing of sectors into a linear LBA model, note that: Cylinder Head Record format has been used by Count Key Data (CKD) hard disks on IBM mainframes since at least the 1960s. This is largely comparable to the Cylinder Head Sector format used by PCs, with
3550-539: The disk, i.e., a cluster can begin at a sector near the end of a given C H track, and end in a sector on the physically or logically next C H track . In 2002 the ATA-6 specification introduced an optional 48 bits Logical Block Addressing and declared CHS addressing as obsolete, but still allowed to implement the ATA-5 translations. Unsurprisingly the CHS to LBA translation formula given below also matches
3621-546: The drive (or the BIOS), since the drive will convert any given CHS value into an actual address for its specific hardware configuration. This however can cause compatibility problems. For operating systems such as Microsoft DOS or older version of Windows , each partition must start and end at a cylinder boundary. Only some of the relatively modern operating systems (Windows XP included) may disregard this rule, but doing so can still cause some compatibility issues, especially if
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#17327768277123692-460: The exception that the sector size was not fixed but could vary from track to track based on the needs of each application. In contemporary use, the disk geometry presented to the mainframe is emulated by the storage firmware, and no longer has any relation to physical disk geometry. Earlier hard drives used in the PC, such as MFM and RLL drives, divided each cylinder into an equal number of sectors, so
3763-505: The figure. The cylindrical surface without the ends is called an open cylinder . The formulae for the surface area and the volume of a right circular cylinder have been known from early antiquity. A right circular cylinder can also be thought of as the solid of revolution generated by rotating a rectangle about one of its sides. These cylinders are used in an integration technique (the "disk method") for obtaining volumes of solids of revolution. A tall and thin needle cylinder has
3834-501: The geometry became more complicated (for example, with the introduction of zone bit recording ) and drive sizes grew over time, the CHS addressing method became restrictive. Since the late 1980s, hard drives began shipping with an embedded disk controller that had good knowledge of the physical geometry; they would however report a false geometry to the computer, e.g., a larger number of heads than actually present, to gain more addressable space. These logical CHS values would be translated by
3905-483: The last ATA-5 CHS translation. In the ATA-5 specification CHS support was mandatory for up to 16 514 064 sectors and optional for larger disks. The ATA-5 limit corresponds to CHS 16383 16 63 or equivalent disk capacities (16514064 = 16383 × 16 × 63 = 1032 × 254 × 63) , and requires 24 = 14 + 4 + 6 bits ( 16383 + 1 = 2 ). CHS tuples can be mapped onto LBA addresses using the following formula: A = ( c × N h e
3976-471: The late 2000s. In the early 2010s, the disk size limitations imposed by MBR became problematic and the GUID Partition Table (GPT) was designed as a replacement; modern computers using UEFI firmware without MBR support no longer use any notions from CHS addressing. CHS addressing is the process of identifying individual sectors (aka. physical block of data) on a disk by their position in
4047-399: The lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. Any line in this family of parallel lines is called an element of the cylindrical surface. From a kinematics point of view, given a plane curve, called the directrix , a cylindrical surface is that surface traced out by a line, called the generatrix , not in
4118-408: The literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the right circular cylinder . The definitions and results in this section are taken from the 1913 text Plane and Solid Geometry by George A. Wentworth and David Eugene Smith ( Wentworth & Smith 1913 ). A cylindrical surface is a surface consisting of all the points on all
4189-451: The maximal sector number is determined by the low level format of the disk. However, for disk access with the BIOS of IBM-PC compatible machines, the sector number was encoded in six bits, resulting in a maximal number of 111111 (63) sectors per track. This maximum is still in use for virtual CHS geometries. The tracks are the thin concentric circular strips of sectors. At least one head
4260-532: The maximum disk size in old BIOS INT 13h code as well as old PC DOS or similar operating systems: (512 bytes/sector)×(63 sectors/track)×(255 heads (tracks/cylinder))×(1024 cylinders)=8032.5 MB , but actually 512×63×256×1024=8064 MB yields what is known as 8 GB limit. In this context relevant definition of 8 GB = 8192 MB is another incorrect limit, because it would require CHS 512×64×256 with 64 sectors per track. Tracks and cylinders are counted from 0, i.e., track 0
4331-417: The number of sectors dividing each track varies with the location of groups of tracks on the surface of the platter. Tracks nearer to the edge of the platter contain more blocks of data than tracks close to the spindle, because there is more physical space within a given track near the edge of the platter. Thus, the CHS addressing scheme cannot correspond directly with the physical geometry of such drives, due to
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#17327768277124402-461: The number of tracks on a single surface in the drive. It comprises the same track number on each platter, spanning all such tracks across each platter surface that is able to store data (without regard to whether or not the track is "bad"). Cylinders are vertically formed by tracks . In other words, track 12 on platter 0 plus track 12 on platter 1 etc. is cylinder 12. Other forms of Direct Access Storage Device (DASD), such as drum memory devices or
4473-410: The physical layout. A separate generic controller card was used, so that the operating system had to know the exact physical "geometry" of the specific drive attached to the controller, to correctly address data blocks. The traditional limits were 512 bytes/sector × 63 sectors/track × 255 heads (tracks/cylinder) × 1024 cylinders, resulting in a limit of 8032.5 MiB for the total capacity of a disk. As
4544-413: The plane of the directrix, moving parallel to itself and always passing through the directrix. Any particular position of the generatrix is an element of the cylindrical surface. A solid bounded by a cylindrical surface and two parallel planes is called a (solid) cylinder . The line segments determined by an element of the cylindrical surface between the two parallel planes is called an element of
4615-438: The solid right circular cylinder is made up the sum of all three components: top, bottom and side. Its surface area is therefore A = L + 2 B = 2 π r h + 2 π r 2 = 2 π r ( h + r ) = π d ( r + h ) {\displaystyle A=L+2B=2\pi rh+2\pi r^{2}=2\pi r(h+r)=\pi d(r+h)} where d = 2 r
4686-729: The term side is substituted for head, since platters might be separated from their head assemblies, as with the removable media of a floppy drive.) The C H S addressing supported in IBM-PC compatible BIOSes code used eight bits for a maximum of 256 heads counted as head 0 up to 255 ( FFh ). However, a bug in all versions of Microsoft DOS / IBM PC DOS up to and including 7.10 will cause these operating systems to crash on boot when encountering volumes with 256 heads. Therefore, all compatible BIOSes will use mappings with up to 255 heads ( 00h..FEh ) only, including in virtual 255×63 geometries. This historical oddity can affect
4757-415: The user wants to perform dual booting on the same drive. Microsoft does not follow this rule with internal disk partition tools since Windows Vista. Cylinder A cylinder (from Ancient Greek κύλινδρος ( kúlindros ) 'roller, tumbler') has traditionally been a three-dimensional solid , one of the most basic of curvilinear geometric shapes . In elementary geometry , it
4828-413: The varying number of sectors per track for different regions on a platter. Because of this, many drives still have a surplus of sectors (less than 1 cylinder in size) at the end of the drive, since the total number of sectors rarely, if ever, ends on a cylinder boundary. An ATA/IDE drive can be set in the system BIOS with any configuration of cylinders, heads and sectors that do not exceed the capacity of
4899-477: The volume of a cylindrical shell equals 2 π × average radius × altitude × thickness. The surface area, including the top and bottom, is given by A = 2 π ( R + r ) h + 2 π ( R 2 − r 2 ) . {\displaystyle A=2\pi \left(R+r\right)h+2\pi \left(R^{2}-r^{2}\right).} Cylindrical shells are used in
4970-554: The volume of a right circular cylinder can be calculated by integration V = ∫ 0 h ∫ 0 2 π ∫ 0 r s d s d ϕ d z = π r 2 h . {\displaystyle {\begin{aligned}V&=\int _{0}^{h}\int _{0}^{2\pi }\int _{0}^{r}s\,\,ds\,d\phi \,dz\\[5mu]&=\pi \,r^{2}\,h.\end{aligned}}} Having radius r and altitude (height) h ,
5041-432: Was 1024×16×63=1032192 sectors, i.e., a 504 MB limit for sector size 512. BIOS translation schemes known as ECHS and revised ECHS mitigated this limitation by using 128 or 240 instead of 16 heads, simultaneously reducing the numbers of cylinders and sectors to fit into 1024/128/63 (ECHS limit: 4032 MB ) or 1024/240/63 (revised ECHS limit: 7560 MB ) for the given total number of sectors on
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