title: Total internal reflection

text: Fresnel's deduction of the phase shift in TIR is thought to have been the first occasion on which a physical meaning was attached to the argument of a complex number. Although this reasoning was applied without the benefit of knowing that light waves were electromagnetic, it passed the test of experiment, and survived remarkably intact after James Clerk Maxwell changed the presumed nature of the waves. Meanwhile, Fresnel's success inspired James MacCullagh and Augustin-Louis Cauchy, beginning in 1836, to analyze reflection from metals by using the Fresnel equations with a complex refractive index. The imaginary part of the complex index represents absorption.


title: Total internal reflection

text: The term "critical angle", used for convenience in the above narrative, is anachronistic: it apparently dates from 1873.


title: Total internal reflection

text: In the 20th century, quantum electrodynamics reinterpreted the amplitude of an electromagnetic wave in terms of the probability of finding a photon. In this framework, partial transmission and frustrated TIR concern the probability of a photon crossing a boundary, and attenuated total reflectance concerns the probability of a photon being absorbed on the other side.


title: Total internal reflection

text: Research into the more subtle aspects of the phase shift in TIR, including the Goos–Hänchen and Imbert–Fedorov effects and their quantum interpretations, has continued into the 21st century.


title: Intel 8086

text: The 8086 (also called iAPX 86) is a 16-bit microprocessor chip designed by Intel between early 1976 and June 8, 1978, when it was released. The Intel 8088, released July 1, 1979, is a slightly modified chip with an external 8-bit data bus (allowing the use of cheaper and fewer supporting ICs), and is notable as the processor used in the original IBM PC design.


title: Intel 8086

text: The 8086 gave rise to the x86 architecture, which eventually became Intel's most successful line of processors. On June 5, 2018, Intel released a limited-edition CPU celebrating the 40th anniversary of the Intel 8086, called the Intel Core i7-8086K.


title: Intel 8086

text: In 1972, Intel launched the 8008, the first 8-bit microprocessor. It implemented an instruction set designed by Datapoint Corporation with programmable CRT terminals in mind, which also proved to be fairly general-purpose. The device needed several additional ICs to produce a functional computer, in part due to it being packaged in a small 18-pin "memory package", which ruled out the use of a separate address bus (Intel was primarily a DRAM manufacturer at the time).


title: Intel 8086

text: Two years later, Intel launched the 8080, employing the new 40-pin DIL packages originally developed for calculator ICs to enable a separate address bus. It has an extended instruction set that is source-compatible (not binary compatible) with the 8008 and also includes some 16-bit instructions to make programming easier. The 8080 device was eventually replaced by the depletion-load-based 8085 (1977), which sufficed with a single +5 V power supply instead of the three different operating voltages of earlier chips. Other well known 8-bit microprocessors that emerged during these years are Motorola 6800 (1974), General Instrument PIC16X (1975), MOS Technology 6502 (1975), Zilog Z80 (1976), and Motorola 6809 (1978).


title: Intel 8086

text: The 8086 project started in May 1976 and was originally intended as a temporary substitute for the ambitious and delayed iAPX 432 project. It was an attempt to draw attention from the less-delayed 16-bit and 32-bit processors of other manufacturers — Motorola, Zilog, and National Semiconductor.


title: Intel 8086

text: Whereas the 8086 was a 16-bit microprocessor, it used the same microarchitecture as Intel's 8-bit microprocessors (8008, 8080, and 8085). This allowed assembly language programs written in 8-bit to seamlessly migrate. New instructions and features — such as signed integers, base+offset addressing, and self-repeating operations — were added. Instructions were added to assist source code compilation of nested functions in the ALGOL-family of languages, including Pascal and PL/M. According to principal architect Stephen P. Morse, this was a result of a more software-centric approach. Other enhancements included microcode instructions for the multiply and divide assembly language instructions. Designers also anticipated coprocessors, such as 8087 and 8089, so the bus structure was designed to be flexible.


title: Intel 8086

text: The first revision of the instruction set and high level architecture was ready after about three months, and as almost no CAD tools were used, four engineers and 12 layout people were simultaneously working on the chip. The 8086 took a little more than two years from idea to working product, which was considered rather fast for a complex design in 1976–1978.


title: Intel 8086

text: The 8086 was sequenced using a mixture of random logic and microcode and was implemented using depletion-load nMOS circuitry with approximately 20,000 active transistors (29,000 counting all ROM and PLA sites). It was soon moved to a new refined nMOS manufacturing process called HMOS (for High performance MOS) that Intel originally developed for manufacturing of fast static RAM products. This was followed by HMOS-II, HMOS-III versions, and, eventually, a fully static CMOS version for battery powered devices, manufactured using Intel's CHMOS processes. The original chip measured 33 mm² and minimum feature size was 3.2 μm.


title: Intel 8086

text: The architecture was defined by Stephen P. Morse with some help from Bruce Ravenel (the architect of the 8087) in refining the final revisions. Logic designer Jim McKevitt and John Bayliss were the lead engineers of the hardware-level development team and Bill Pohlman the manager for the project. The legacy of the 8086 is enduring in the basic instruction set of today's personal computers and servers; the 8086 also lent its last two digits to later extended versions of the design, such as the Intel 286 and the Intel 386, all of which eventually became known as the x86 family. (Another reference is that the PCI Vendor ID for Intel devices is 8086.)


title: Intel 8086

text: All internal registers, as well as internal and external data buses, are 16 bits wide, which firmly established the "16-bit microprocessor" identity of the 8086. A 20-bit external address bus provides a 1 MB physical address space (2 = 1,048,576 x 1 byte). This address space is addressed by means of internal memory "segmentation". The data bus is multiplexed with the address bus in order to fit all of the control lines into a standard 40-pin dual in-line package. It provides a 16-bit I/O address bus, supporting 64 KB of separate I/O space. The maximum linear address space is limited to 64 KB, simply because internal address/index registers are only 16 bits wide. Programming over 64 KB memory boundaries involves adjusting the segment registers (see below); this difficulty existed until the 80386 architecture introduced wider (32-bit) registers (the memory management hardware in the 80286 did not help in this regard, as its registers are still only 16 bits wide).


title: Intel 8086

text: Some of the control pins, which carry essential signals for all external operations, have more than one function depending upon whether the device is operated in "min" or "max" mode. The former mode is intended for small single-processor systems, while the latter is for medium or large systems using more than one processor (a kind of multiprocessor mode). Maximum mode is required when using an 8087 or 8089 coprocessor. The voltage on pin 33 (MN/) determines the mode. Changing the state of pin 33 changes the function of certain other pins, most of which have to do with how the CPU handles the (local) bus. The mode is usually hardwired into the circuit and therefore cannot be changed by software. The workings of these modes are described in terms of timing diagrams in Intel datasheets and manuals. In minimum mode, all control signals are generated by the 8086 itself.


title: Intel 8086

text: The 8086 has eight more or less general 16-bit registers (including the stack pointer but excluding the instruction pointer, flag register and segment registers). Four of them, AX, BX, CX, DX, can also be accessed as twice as many 8-bit registers (see figure) while the other four, SI, DI, BP, SP, are 16-bit only.


title: Intel 8086

text: Due to a compact encoding inspired by 8-bit processors, most instructions are one-address or two-address operations, which means that the result is stored in one of the operands. At most one of the operands can be in memory, but this memory operand can also be the "destination", while the other operand, the "source", can be either "register" or "immediate". A single memory location can also often be used as both "source" and "destination" which, among other factors, further contributes to a code density comparable to (and often better than) most eight-bit machines at the time.


title: Intel 8086

text: The degree of generality of most registers is much greater than in the 8080 or 8085. However, 8086 registers were more specialized than in most contemporary minicomputers and are also used implicitly by some instructions. While perfectly sensible for the assembly programmer, this makes register allocation for compilers more complicated compared to more orthogonal 16-bit and 32-bit processors of the time such as the PDP-11, VAX, 68000, 32016, etc. On the other hand, being more regular than the rather minimalistic but ubiquitous 8-bit microprocessors such as the 6502, 6800, 6809, 8085, MCS-48, 8051, and other contemporary accumulator-based machines, it is significantly easier to construct an efficient code generator for the 8086 architecture.


title: Intel 8086

text: Another factor for this is that the 8086 also introduced some new instructions (not present in the 8080 and 8085) to better support stack-based high-level programming languages such as Pascal and PL/M; some of the more useful instructions are codice_1, and ret "size", supporting the "Pascal calling convention" directly. (Several others, such as codice_2 and codice_3, were added in the subsequent 80186, 80286, and 80386 processors.)


title: Intel 8086

text: A 64 KB (one segment) stack growing towards lower addresses is supported in hardware; 16-bit words are pushed onto the stack, and the top of the stack is pointed to by SS:SP. There are 256 interrupts, which can be invoked by both hardware and software. The interrupts can cascade, using the stack to store the return addresses.


title: Intel 8086

text: The 8086 has a 16-bit flags register. Nine of these condition code flags are active, and indicate the current state of the processor: Carry flag (CF), Parity flag (PF), Auxiliary carry flag (AF), Zero flag (ZF), Sign flag (SF), Trap flag (TF), Interrupt flag (IF), Direction flag (DF), and Overflow flag (OF).


title: Intel 8086

text: There are also four 16-bit segment registers (see figure) that allow the 8086 CPU to access one megabyte of memory in an unusual way. Rather than concatenating the segment register with the address register, as in most processors whose address space exceeds their register size, the 8086 shifts the 16-bit segment only four bits left before adding it to the 16-bit offset (16×segment + offset), therefore producing a 20-bit external (or effective or physical) address from the 32-bit segment:offset pair. As a result, each external address can be referred to by 2 = 4096 different segment:offset pairs.


title: Intel 8086

text: Although considered complicated and cumbersome by many programmers, this scheme also has advantages; a small program (less than 64 KB) can be loaded starting at a fixed offset (such as 0000) in its own segment, avoiding the need for relocation, with at most 15 bytes of alignment waste.


title: Intel 8086

text: Compilers for the 8086 family commonly support two types of pointer, "near" and "far". Near pointers are 16-bit offsets implicitly associated with the program's code or data segment and so can be used only within parts of a program small enough to fit in one segment. Far pointers are 32-bit segment:offset pairs resolving to 20-bit external addresses. Some compilers also support "huge" pointers, which are like far pointers except that pointer arithmetic on a huge pointer treats it as a linear 20-bit pointer, while pointer arithmetic on a far pointer wraps around within its 16-bit offset without touching the segment part of the address.


title: Intel 8086

text: To avoid the need to specify "near" and "far" on numerous pointers, data structures, and functions, compilers also support "memory models" which specify default pointer sizes. The "tiny" (max 64K), "small" (max 128K), "compact" (data > 64K), "medium" (code > 64K), "large" (code,data > 64K), and "huge" (individual arrays > 64K) models cover practical combinations of near, far, and huge pointers for code and data. The "tiny" model means that code and data are shared in a single segment, just as in most 8-bit based processors, and can be used to build ".com" files for instance. Precompiled libraries often come in several versions compiled for different memory models.


title: Intel 8086

text: According to Morse et al.. the designers actually contemplated using an 8-bit shift (instead of 4-bit), in order to create a 16 MB physical address space. However, as this would have forced segments to begin on 256-byte boundaries, and 1 MB was considered very large for a microprocessor around 1976, the idea was dismissed. Also, there were not enough pins available on a low cost 40-pin package for the additional four address bus pins.


title: Intel 8086

text: In principle, the address space of the x86 series "could" have been extended in later processors by increasing the shift value, as long as applications obtained their segments from the operating system and did not make assumptions about the equivalence of different segment:offset pairs. In practice the use of "huge" pointers and similar mechanisms was widespread and the flat 32-bit addressing made possible with the 32-bit offset registers in the 80386 eventually extended the limited addressing range in a more general way.


title: Intel 8086

text: The instruction stream is fetched from memory as words and is addressed internally by the processor to the byte level as necessary. An instruction stream queuing mechanism allows up to 6 bytes of the instruction stream to be queued while waiting for decoding and execution. The queue acts as a First-In-First-Out (FIFO) buffer, from which the Execution Unit (EU) extracts instruction bytes as required. Whenever there is space for at least two bytes in the queue, the BIU will attempt a word fetch memory cycle. If the queue is empty (following a branch instruction, for example), the first byte into the queue immediately becomes available to the EU.


title: Intel 8086

text: Small programs could ignore the segmentation and just use plain 16-bit addressing. This allows 8-bit software to be quite easily ported to the 8086. The authors of most DOS implementations took advantage of this by providing an Application Programming Interface very similar to CP/M as well as including the simple ".com" executable file format, identical to CP/M. This was important when the 8086 and MS-DOS were new, because it allowed many existing CP/M (and other) applications to be quickly made available, greatly easing acceptance of the new platform.


title: Intel 8086

text: The following 8086/8088 assembler source code is for a subroutine named codice_4 that copies a block of data bytes of a given size from one location to another. The data block is copied one byte at a time, and the data movement and looping logic utilizes 16-bit operations.


title: Intel 8086

text: The code above uses the BP (base pointer) register to establish a call frame, an area on the stack that contains all of the parameters and local variables for the execution of the subroutine. This kind of calling convention supports reentrant and recursive code, and has been used by most ALGOL-like languages since the late 1950s.


title: Intel 8086

text: The above routine is a rather cumbersome way to copy blocks of data. The 8086 provides dedicated instructions for copying strings of bytes. These instructions assume that the source data is stored at DS:SI, the destination data is stored at ES:DI, and that the number of elements to copy is stored in CX. The above routine requires the source and the destination block to be in the same segment, therefore DS is copied to ES. The loop section of the above can be replaced by:


title: Intel 8086

text: This copies the block of data one byte at a time. The codice_5 instruction causes the following codice_6 to repeat until CX is zero, automatically incrementing SI and DI and decrementing CX as it repeats. Alternatively the codice_7 instruction can be used to copy 16-bit words (double bytes) at a time (in which case CX counts the number of words copied instead of the number of bytes). Most assemblers will properly recognize the codice_5 instruction if used as an in-line prefix to the codice_6 instruction, as in codice_10.


title: Intel 8086

text: This routine will operate correctly if interrupted, because the program counter will continue to point to the codice_5 instruction until the block copy is completed. The copy will therefore continue from where it left off when the interrupt service routine returns control.


title: Intel 8086

text: Although partly shadowed by other design choices in this particular chip, the multiplexed address and data buses limit performance slightly; transfers of 16-bit or 8-bit quantities are done in a four-clock memory access cycle, which is faster on 16-bit, although slower on 8-bit quantities, compared to many contemporary 8-bit based CPUs. As instructions vary from one to six bytes, fetch and execution are made concurrent and decoupled into separate units (as it remains in today's x86 processors): The "bus interface unit" feeds the instruction stream to the "execution unit" through a 6-byte prefetch queue (a form of loosely coupled pipelining), speeding up operations on registers and immediates, while memory operations became slower (four years later, this performance problem was fixed with the 80186 and 80286). However, the full (instead of partial) 16-bit architecture with a full width ALU meant that 16-bit arithmetic instructions could now be performed with a single ALU cycle (instead of two, via internal carry, as in the 8080 and 8085), speeding up such instructions considerably. Combined with orthogonalizations of operations versus operand types and addressing modes, as well as other enhancements, this made the performance gain over the 8080 or 8085 fairly significant, despite cases where the older chips may be faster (see below).


title: Intel 8086

text: As can be seen from these tables, operations on registers and immediates were fast (between 2 and 4 cycles), while memory-operand instructions and jumps were quite slow; jumps took more cycles than on the simple 8080 and 8085, and the 8088 (used in the IBM PC) was additionally hampered by its narrower bus. The reasons why most memory related instructions were slow were threefold:


title: Intel 8086

text: However, memory access performance was drastically enhanced with Intel's next generation of 8086 family CPUs. The 80186 and 80286 both had dedicated address calculation hardware, saving many cycles, and the 80286 also had separate (non-multiplexed) address and data buses.


title: Intel 8086

text: The 8086/8088 could be connected to a mathematical coprocessor to add hardware/microcode-based floating-point performance. The Intel 8087 was the standard math coprocessor for the 8086 and 8088, operating on 80-bit numbers. Manufacturers like Cyrix (8087-compatible) and Weitek ("not" 8087-compatible) eventually came up with high-performance floating-point coprocessors that competed with the 8087.


title: Intel 8086

text: The clock frequency was originally limited to 5 MHz, but the last versions in HMOS were specified for 10 MHz. HMOS-III and CMOS versions were manufactured for a long time (at least a while into the 1990s) for embedded systems, although its successor, the 80186/80188 (which includes some on-chip peripherals), has been more popular for embedded use.


title: Intel 8086

text: The 80C86, the CMOS version of the 8086, was used in the GRiDPad, Toshiba T1200, HP 110, and finally the 1998–1999 Lunar Prospector.


title: Intel 8086

text: Compatible—and, in many cases, enhanced—versions were manufactured by Fujitsu, Harris/Intersil, OKI, Siemens, Texas Instruments, NEC, Mitsubishi, and AMD. For example, the NEC V20 and NEC V30 pair were hardware-compatible with the 8088 and 8086 even though NEC made original Intel clones μPD8088D and μPD8086D respectively, but incorporated the instruction set of the 80186 along with some (but not all) of the 80186 speed enhancements, providing a drop-in capability to upgrade both instruction set and processing speed without manufacturers having to modify their designs. Such relatively simple and low-power 8086-compatible processors in CMOS are still used in embedded systems.


title: Intel 8086

text: The electronics industry of the Soviet Union was able to replicate the 8086 through . The resulting chip, K1810VM86, was binary and pin-compatible with the 8086.


title: Intel 8086

text: i8086 and i8088 were respectively the cores of the Soviet-made PC-compatible EC1831 and EC1832 desktops. (EC1831 is the EC identification of IZOT 1036C and EC1832 is the EC identification of IZOT 1037C, developed and manufactured in Bulgaria. EC stands for Единая Система.) However, the EC1831 computer (IZOT 1036C) had significant hardware differences from the IBM PC prototype. The EC1831 was the first PC-compatible computer with dynamic bus sizing (US Pat. No 4,831,514). Later some of the EC1831 principles were adopted in PS/2 (US Pat. No 5,548,786) and some other machines (UK Patent Application, Publication No. GB-A-2211325, Published June 28, 1989).


title: Mike Conley Jr.

text: Michael Alex Conley Jr. (born October 11, 1987) is an American professional basketball player for the Utah Jazz of the National Basketball Association (NBA). He was drafted as the fourth pick in the 2007 NBA draft by the Memphis Grizzlies. Conley spent 12 seasons with the Grizzlies and become the team's all time leading scorer before being traded to the Jazz in 2019.


title: Mike Conley Jr.

text: Conley attended Lawrence North High School in Indianapolis, where he led the basketball team to three consecutive state championships and an overall record of in his four years as the starting point guard. Over his senior year, he recorded a total of 123 assists. He finished second in Indiana Mr. Basketball voting behind teammate Greg Oden, who was the national player of the year. Among other accolades, Conley was selected to the McDonald's All American Team and named to the "Parade" All-American Third Team.


title: Mike Conley Jr.

text: Considered a five-star recruit by Rivals.com, Conley was listed as the No. 3 point guard and the No. 18 player in the nation in 2006. He committed to Ohio State University as one part of the number two recruiting class in the country that year, along with fellow AAU teammates Greg Oden, Daequan Cook, and Mark Titus.


title: Mike Conley Jr.

text: In his freshman year at Ohio State, Conley averaged 11.3 points and led the Big Ten Conference in assists with 6.1 per game. Conley, together with fellow freshman star Greg Oden, led the Buckeyes to a Big Ten conference championship and a runner-up finish in the NCAA Tournament.


title: Mike Conley Jr.

text: On the road to the championship game, the Buckeyes defeated Central Connecticut State, Xavier, Tennessee, Memphis, and Georgetown, only to lose in the championship game to the repeat national champions Florida. Conley's best performance in the tournament came in the contest against Xavier. He recorded 21 points, 4 assists, 2 steals, and 3 blocks as Ohio State defeated the Musketeers in overtime. Greg Oden fouled out in regulation, and Conley scored 11 of his 21 points in the extra period to lead the Buckeyes to a victory.


title: Mike Conley Jr.

text: Ending the season with totals of 441 points and 238 assists, Conley was named to the All-Big Ten First Team.


title: Mike Conley Jr.

text: Following his freshman season, Conley announced his intention to enter the 2007 NBA draft along with Oden. He initially did not sign with an agent in order to preserve his eligibility to withdraw from the draft but ended up signing with his father several weeks before the draft.


title: Mike Conley Jr.

text: Conley joined fellow Buckeyes Greg Oden and Daequan Cook in declaring for the 2007 NBA draft; both Conley and Oden were represented by Conley's father, whom the NBA certified as an agent earlier in the year. Conley was drafted by the Memphis Grizzlies as the fourth overall pick after Greg Oden, Kevin Durant, and Al Horford.


title: Mike Conley Jr.

text: Conley had his first major appearances in January 2008. In Conley's first five career games, he scored 5, 10, 11, 11, and 15 points, respectively. He scored a season-high 20 points with 7 assists in a 134–124 loss to the Cleveland Cavaliers. Conley finished his rookie year with averages of 9.4 points and 4.2 assists per game.


title: Mike Conley Jr.

text: Conley started his sophomore campaign competing with Kyle Lowry for minutes. On January 25, 2009, the Grizzlies made Lionel Hollins the head coach after the firing of Marc Iavaroni. On February 19, 2009, Lowry was traded to the Houston Rockets, which put Conley in the starting lineup. He averaged 10.8 points and 4.3 assists per game for the year.


title: Mike Conley Jr.

text: Conley cemented his role as a full-time starter for the Grizzlies in 2009. He posted a season-high of 25 points on March 31, 2010, during a 102–106 loss to the Dallas Mavericks. He averaged 12.0 points and 5.3 assists on the season.


title: Mike Conley Jr.

text: On November 30, Conley put up a season-high 28 points in a 98–96 victory over the Los Angeles Lakers. Conley averaged 13.7 and 6.5 assists on the year to help the Grizzlies make the playoffs for the first time in five years. Entering with the eighth seed in the Western Conference, they were matched up in the first round with the top-seeded San Antonio Spurs. Conley and the Grizzlies went on to defeat the Spurs in six games and make NBA history as only the second eighth-seeded team to defeat a first seed in a seven-game series. They then lost to the Oklahoma City Thunder in the Semifinals after seven games.


title: Mike Conley Jr.

text: In the shortened lockout season, Conley played 62 of the Grizzlies' 66 games, during which he averaged 12.7 points and 6.5 assists. Conley and the Grizzlies would make the playoffs but fell in the first round to the Los Angeles Clippers in seven games.


title: Mike Conley Jr.

text: On the year, Conley averaged 14.6 points, 6.1 assists, and 2.8 rebounds per game as the Grizzlies made the playoffs once again. They eliminated the Los Angeles Clippers and the Oklahoma City Thunder to reach the Western Conference Finals for the first time in franchise history. However, they then lost to the San Antonio Spurs in four games. It was in this season that Conley was named to the NBA All-Defensive Second Team for the first time.


title: Mike Conley Jr.

text: Conley averaged a career-high 17.2 points, 6.0 assists, and 2.9 rebounds per game on the year as the Grizzles made the playoffs for the fourth consecutive season. They were then eliminated in the first round by the Oklahoma City Thunder in a seven game series. Conley was the recipient of the NBA Sportsmanship Award.


title: Mike Conley Jr.

text: On December 13, 2014, Conley scored a career-high 36 points to help the Grizzlies defeat the Philadelphia 76ers, 120–115, in overtime. The Grizzlies finished the season as the fifth seed in the Western Conference, making the playoffs once again. They then faced the Portland Trail Blazers in the first round and defeated them in five games. Near the end of Game Three of the series, Conley suffered a facial fracture, which forced him to miss the rest of the first round. He also missed Game One of the Semifinals against the Golden State Warriors. But Conley returned in Game Two of the series; and, while donning a protective mask, he scored 21 points to lead Memphis to a victory. However, Memphis eventually lost to the Warriors in six games.


title: Mike Conley Jr.

text: In 2014, Conley received what would have been the first technical foul of his NBA career, but it was overturned by league officials the following day; as of January 2020 he has yet to record a technical, having by far the longest streak without one of any NBA player.


title: Mike Conley Jr.

text: On October 31, 2015, Conley surpassed Shareef Abdur-Rahim (7,801) for third on the Grizzlies' career scoring list. He scored 22 points against the Brooklyn Nets to finish the game with 7,821 career points. On January 18, 2016, Conley returned to the lineup after missing six games with a sore left Achilles and recorded his third double-double of the season with 15 points and 10 assists, helping the Grizzlies defeat the New Orleans Pelicans 101–99. Earlier that day, he was named one of the 30 finalists for the 2016 U.S. Olympic team. On March 12, he was ruled out for three to four weeks with a left foot injury. He was later ruled out for the rest of the season on April 4 following a re-evaluation by team doctors, and hoping to return during playoffs. The injury-riddled Grizzlies finished seventh in the Western Conference, and without Conley and Marc Gasol, they were swept by the San Antonio Spurs in the first round of the playoffs. On April 23, Conley was awarded the NBA Sportsmanship Award for the second time.


title: Mike Conley Jr.

text: On July 14, 2016, Conley re-signed with the Grizzlies. His reported five-year, $153 million deal was the greatest contract by total value in NBA history at that point in time. On November 16, 2016, he scored 30 points and hit a career-high-tying seven three-pointers in a 111–107 win over the Los Angeles Clippers. On November 29, he was ruled out for six to eight weeks with a fractured vertebrae. He returned to action on December 16 after missing nine games. In the Grizzlies' 96–92 loss to the Sacramento Kings, Conley passed Pau Gasol to become the all-time leading scorer in Grizzlies franchise history. On January 30, 2017, he scored 38 points in a 115–98 win over the Phoenix Suns. Conley matched his career best with seven three-pointers (in 10 attempts) and made 12 of 18 shots overall in his fourth 30-point game of the season—he previously had just five over his entire career. On February 15 against New Orleans, Conley passed Mike Miller for the most three-pointers in franchise history with 845. On March 29, he matched his career-high with seven three-pointers on his way to 36 points, helping the Grizzlies rout the Indiana Pacers 110–97.


title: Mike Conley Jr.

text: On April 22, 2017, Conley scored a franchise postseason record 35 points in a 110–108 overtime win over the San Antonio Spurs. The win tied the first-round series at 2–2.


title: Mike Conley Jr.

text: Conley appeared in 12 of the Grizzlies' first 13 games of the 2017–18 season before suffering a left Achilles injury. On January 27, 2018, he was ruled out for the rest of the season after requiring surgery to smooth a small bone protrusion in his left heel.


title: Mike Conley Jr.

text: In the Grizzlies' season opener on October 17, 2018, Conley made his first regular season appearance since November 2017 after missing 70 games in 2017–18. He played nearly 29 minutes, scored 11 points and had three assists and one steal in a 111–83 loss to the Indiana Pacers. On November 2, he scored a season-high 28 points in a 110–100 win over the Utah Jazz. On November 10, he set a new season-high with 32 points in a 112–106 overtime win over the Philadelphia 76ers. On November 30, Conley improved his season-high scoring to 37 points and also made 10 assists in a 131–125 double-overtime win over the Brooklyn Nets. On March 5, 2019, Conley scored a career-high 40 points in a Grizzlies' 120–111 win over the Portland Trail Blazers. He was scoreless in the first quarter, Conley scored 19 of his career-high 40 points in the fourth quarter. On March 11, he was named Western Conference Player of the Week for games played from March 4 to March 10. It marked his first career Player of the Week award. On March 27, in a 118–103 loss to the Golden State Warriors, Conley passed Marc Gasol to become the Grizzlies' all-time leader in career points.


title: Mike Conley Jr.

text: On July 6, 2019, the Grizzlies announced that they had traded Conley to the Utah Jazz in exchange for Grayson Allen, Jae Crowder, Kyle Korver, the draft rights to Darius Bazley, and a protected first round pick. After the 2019–20 season, Conley declined to exercise the early termination option on his contract, and he was owed $34.5 million in the fifth and final year of his contract in 2020–21.


title: Mike Conley Jr.

text: In 2020, due to the suspension of the NBA season because of the COVID-19 pandemic, the NBA produced a televised event in which NBA and WNBA players participated in a virtual H–O–R–S–E competition while quarantining at their respective homes. The NBA raised $200,000 for charities while Conley of the Utah Jazz won the first virtual NBA H–O–R–S–E Competition, to become the inaugural "H.O.R.S.E Champion".


title: Mike Conley Jr.

text: On January 1, 2021, Conley scored 33 points and added seven assists, two rebounds, and one steal in a 106–100 win against the Los Angeles Clippers. On August 2, 2021, it was announced that Conley re-signed with the Utah Jazz on a three-year deal.


title: Mike Conley Jr.

text: In his 14th NBA season, Conley was named an All-Star for the first time in his career as it was announced that he would be a reserve for the 2021 NBA All-Star Game, replacing the injured Devin Booker. His 14-year wait is the longest ever for a first time All-Star. He recorded three points, one rebound, and two assists in 12 minutes in the game. Conley was also announced as Booker's replacement in the Three-Point Contest, where he competed against teammate Donovan Mitchell. Conley lost in the final round to Stephen Curry, 28–27.


title: Mike Conley Jr.

text: Conley is a Christian and has spoken about his faith, saying, "Jesus means the world. Jesus means everything."


title: Mike Conley Jr.

text: Conley's father is Mike Conley Sr., an Olympic gold and silver medalist in the triple jump. He is also the nephew of former American football linebacker Steve Conley.


title: Mike Conley Jr.

text: On July 5, 2014, Conley married his girlfriend Mary Peluso, whom he met at Ohio State. The couple have three sons together.


title: Richard Farnsworth

text: Richard William Farnsworth (September 1, 1920 – October 6, 2000) was an American actor and stuntman. He was twice nominated for an Academy Award: in 1978 for Best Supporting Actor for "Comes a Horseman," and in 2000 for Best Actor in "The Straight Story", making him the oldest nominee for the award at the time. Farnsworth was also known for his performances in "The Grey Fox" (1982), for which he received a Golden Globe Award nomination for Best Actor in a Motion Picture - Drama, as well as "Anne of Green Gables" (1985); Sylvester (1985), and "Misery" (1990).


title: Richard Farnsworth

text: Farnsworth was born on September 1, 1920, in Los Angeles, California. His mother was a homemaker and his father was an engineer.


title: Richard Farnsworth

text: Farnsworth gradually moved into acting in Western movies. He made uncredited appearances in numerous films, including "Gone with the Wind" (1939), "Red River" (1948), "The Wild One" (1953), and "The Ten Commandments" (1956). In 1960, credited as Dick Farnsworth, he appeared as a Gault ranch hand in the "Street of Hate" episode of the TV Western "Laramie".


title: Richard Farnsworth

text: He received his first acting credit in 1963 and went on to act in Western films and television shows. He had a role in "Roots" (1977) and co-starred with Wilford Brimley in "The Boys of Twilight" (1992). His breakthrough came when he played stagecoach robber Bill Miner in the 1982 Canadian film",The Grey Fox". He appeared as a baseball coach in "The Natural" (1984). In 1985, he was the brother to Marilla and father figure to Anne in "Anne of Green Gables" and starred as a soft-spoken, sage cowboy with horse training wisdom for Melissa Gilbert in "Sylvester". His other prominent roles included a wealthy and ruthless oil man in "The Two Jakes" (1990) and the suspicious sheriff in the film version of Stephen King's "Misery" (1990).


title: Richard Farnsworth

text: Farnsworth had a long marriage and had two children. After becoming a widower, he lived on a ranch in Lincoln, New Mexico.


title: Richard Farnsworth

text: On the night of October 6, 2000, suffering from terminal cancer that left him partially paralyzed and in great pain, Farnsworth died from a self-inflicted gunshot wound at his ranch in Lincoln, New Mexico. He is interred at Forest Lawn Memorial Park in the Hollywood Hills of Los Angeles in the Columbarium of Purity (N-63294) beside his wife, Margaret (née Hill).


title: Richard Farnsworth

text: Note: Farnsworth was inducted into the Hall of Great Western Performers at the National Cowboy & Western Heritage Museum in Oklahoma City, Oklahoma, in 1997. In addition, Farnsworth received a Hollywood Walk of Fame star for his contributions in the motion pictures on August 17, 1992; the star is located at 1560 Vine Street.


title: Multinomial distribution

text: In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a "k"-sided dice rolled "n" times. For "n" independent trials each of which leads to a success for exactly one of "k" categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories.


title: Multinomial distribution

text: When "k" is 2 and "n" is 1, the multinomial distribution is the Bernoulli distribution. When "k" is 2 and "n" is bigger than 1, it is the binomial distribution. When "k" is bigger than 2 and "n" is 1, it is the categorical distribution. The term "multinoulli" is sometimes used for the categorical distribution to emphasize this four-way relationship (so "n" determines the prefix, and "k" the suffix).


title: Multinomial distribution

text: The Bernoulli distribution models the outcome of a single Bernoulli trial. In other words, it models whether flipping a (possibly biased) coin one time will result in either a success (obtaining a head) or failure (obtaining a tail). The binomial distribution generalizes this to the number of heads from performing "n" independent flips (Bernoulli trials) of the same coin. The multinomial distribution models the outcome of "n" experiments, where the outcome of each trial has a categorical distribution, such as rolling a "k"-sided dice "n" times.


title: Multinomial distribution

text: Let "k" be a fixed finite number. Mathematically, we have "k" possible mutually exclusive outcomes, with corresponding probabilities "p", ..., "p", and "n" independent trials. Since the "k" outcomes are mutually exclusive and one must occur we have "p" ≥ 0 for "i" = 1, ..., "k" and formula_1. Then if the random variables "X" indicate the number of times outcome number "i" is observed over the "n" trials, the vector "X" = ("X", ..., "X") follows a multinomial distribution with parameters "n" and p, where p = ("p", ..., "p"). While the trials are independent, their outcomes "X" are dependent because they must be summed to n.


title: Multinomial distribution

text: Suppose one does an experiment of extracting "n" balls of "k" different colors from a bag, replacing the extracted balls after each draw. Balls of the same color are equivalent. Denote the variable which is the number of extracted balls of color "i" ("i" = 1, ..., "k") as "X", and denote as "p" the probability that a given extraction will be in color "i". The probability mass function of this multinomial distribution is:


title: Multinomial distribution

text: Suppose that in a three-way election for a large country, candidate A received 20% of the votes, candidate B received 30% of the votes, and candidate C received 50% of the votes. If six voters are selected randomly, what is the probability that there will be exactly one supporter for candidate A, two supporters for candidate B and three supporters for candidate C in the sample?


title: Multinomial distribution

text: "Note: Since we’re assuming that the voting population is large, it is reasonable and permissible to think of the probabilities as unchanging once a voter is selected for the sample. Technically speaking this is sampling without replacement, so the correct distribution is the multivariate hypergeometric distribution, but the distributions converge as the population grows large in comparison to a fixed sample size""."


title: Multinomial distribution

text: The covariance matrix is as follows. Each diagonal entry is the variance of a binomially distributed random variable, and is therefore


title: Multinomial distribution

text: All covariances are negative because for fixed "n", an increase in one component of a multinomial vector requires a decrease in another component.


title: Multinomial distribution

text: When these expressions are combined into a matrix with "i, j" element formula_8 the result is a "k" × "k" positive-semidefinite covariance matrix of rank "k" − 1. In the special case where "k" = "n" and where the "p" are all equal, the covariance matrix is the centering matrix.


title: Multinomial distribution

text: Each of the "k" components separately has a binomial distribution with parameters "n" and "p", for the appropriate value of the subscript "i".


title: Multinomial distribution

text: Just like one can interpret the binomial distribution as (normalized) one-dimensional (1D) slices of Pascal's triangle, so too can one interpret the multinomial distribution as 2D (triangular) slices of Pascal's pyramid, or 3D/4D/+ (pyramid-shaped) slices of higher-dimensional analogs of Pascal's triangle. This reveals an interpretation of the range of the distribution: discretized equilateral "pyramids" in arbitrary dimension—i.e. a simplex with a grid.


title: Multinomial distribution

text: Similarly, just like one can interpret the binomial distribution as the polynomial coefficients of formula_15 when expanded, one can interpret the multinomial distribution as the coefficients of formula_16 when expanded, noting that just the coefficients must sum up to 1.


title: Multinomial distribution

text: In some fields such as natural language processing, categorical and multinomial distributions are synonymous and it is common to speak of a multinomial distribution when a categorical distribution is actually meant. This stems from the fact that it is sometimes convenient to express the outcome of a categorical distribution as a "1-of-K" vector (a vector with one element containing a 1 and all other elements containing a 0) rather than as an integer in the range formula_17; in this form, a categorical distribution is equivalent to a multinomial distribution over a single trial.


title: Multinomial distribution

text: The goal of equivalence testing is to establish the agreement between a theoretical multinomial distribution and observed counting frequencies. The theoretical distribution may be a fully specified multinomial distribution or a parametric family of multinomial distributions.


title: Multinomial distribution

text: Let formula_19 denote a theoretical multinomial distribution and let formula_20 be a true underlying distribution. The distributions formula_20 and formula_19 are considered equivalent if formula_23 for a distance formula_24 and a tolerance parameter formula_25. The equivalence test problem is formula_26 versus formula_27. The true underlying distribution formula_20 is unknown. Instead, the counting frequencies formula_29 are observed, where formula_30 is a sample size. An equivalence test uses formula_29 to reject formula_32. If formula_32 can be rejected then the equivalence between formula_20 and formula_19 is shown at a given significance level. The equivalence test for Euclidean distance can be found in text book of Wellek (2010). The equivalence test for the total variation distance is developed in Ostrovski (2017). The exact equivalence test for the specific cumulative distance is proposed in Frey (2009).


title: Multinomial distribution

text: The distance between the true underlying distribution formula_20 and a family of the multinomial distributions formula_37 is defined by formula_38. Then the equivalence test problem is given by formula_39 and formula_40. The distance formula_41 is usually computed using numerical optimization. The tests for this case are developed recently in Ostrovski (2018).


title: Multinomial distribution

text: First, reorder the parameters formula_42 such that they are sorted in descending order (this is only to speed up computation and not strictly necessary). Now, for each trial, draw an auxiliary variable "X" from a uniform (0, 1) distribution. The resulting outcome is the component


title: Nash Bridges

text: Nash Bridges is an American police procedural television series created by Carlton Cuse. The show stars Don Johnson and Cheech Marin as two Inspectors with the San Francisco Police Department's Special Investigations Unit (SIU).


title: Nash Bridges

text: The series ran for six seasons on CBS from March 29, 1996, to May 4, 2001. A total of 122 episodes aired.


title: Nash Bridges

text: "Nash Bridges" stars Don Johnson as the eponymous Nash Bridges, an inspector (and later captain) with the San Francisco Police Department's elite "Special Investigations Unit". The show begins with Bridges in his 40s, twice-divorced, and dealing with his feisty teenage daughter Cassidy (Jodi Lyn O'Keefe). Nash convinces recently retired Inspector Joe Dominguez (Cheech Marin), to return to the force and partner with him. Nash and Joe cruise the streets of San Francisco in Nash's 1971 Plymouth Barracuda convertible, a gift from Nash's brother Bobby just before Bobby left for the Vietnam War. The car was originally to be painted Curious Yellow, but was switched to factory Caterpillar Yellow, due to lighting and camera appearances. The car is a replica of the infamous 1971 Hemi 'Cuda convertible.


title: Nash Bridges

text: Bobby Bridges was reported as MIA, but turns up in the season 3 episode "Revelations", played by Jan-Michael Vincent. Nash's father, Nick (James Gammon), suffers from mild dementia and has a habit of getting kicked out of nursing homes. He eventually moves in with Nash, and is often involved in comic subplots that are intertwined with some of the show's dark humor themes.


title: Nash Bridges

text: Aiding Nash in his police work is the technically savvy Harvey Leek (Jeff Perry), a middle-aged "Deadhead" (a die hard Grateful Dead fan). Another is the young, hotheaded Evan Cortez (Jaime P. Gomez), who has an off-and-on relationship with Cassidy. In later seasons, other inspectors and supporting characters were added or removed from the cast.


title: Nash Bridges

text: For the first sixteen episodes, the commander of the SIU was Lieutenant A. J. Shimamura (Cary-Hiroyuki Tagawa), a character who was said to have returned to his native Hawaii after failing to be promoted to captain. Shimamura's departure opened the door for Bridges to be promoted to captain and given command of the SIU.


title: Nash Bridges

text: The show was produced and filmed on location in the San Francisco Bay Area. The show shot on the streets of San Francisco including The Embarcadero and Piers 30 through 32. Neighboring Treasure Island was used as the headquarters for the show. Hangar 2 on Treasure Island was the location of permanent sets including Nash's apartment The show employed several hundred local workers including production crews and staff members, carpenters, electricians, set designers, grips, set dressers, props, scenic artists, location managers, costumers, drivers, cameramen, special effects, soundmen, makeup and hair stylists and production assistants. Episode production was nearly $2 million per episode.


title: Nash Bridges

text: The show was produced by the Don Johnson Company and Carlton Cuse Productions in association with Rysher Entertainment for the first 4 seasons. In 1999, Paramount Network Television took over Rysher's spot after acquiring that company.


title: Nash Bridges

text: The show used three different main theme songs during its initial run. Season 1 used primarily an instrumental piece written by Elia Cmíral. Seasons 2–5 used the theme "I Got a Friend In You" written by Eddie Jobson" and sung by Gigi MacKenzie and is by far the most well known of the show's opening themes. Season 6 changed the theme again, using another primarily instrumental piece with a bit of a techno beat to it, this time written by Velton Ray Bunch. A fourth song, also written by Cmíral which was Johnson's original choice, sometimes replaces the first season song in syndication.


title: Nash Bridges

text: The sixth season of "Nash Bridges" would be its last; however, the show was obtaining fair ratings from Nielsen. Following its Friday night ratings battle (which it was losing to NBC's ""), the show was canceled. Paramount Network Television, which was producing the show, felt that its $2 million per episode production cost was just too much. CBS was hoping to get a seventh season out of "Nash Bridges", but that failed because Paramount wasn't willing to pay, even though at the time, Viacom owned both CBS and Paramount.


title: Nash Bridges

text: Another factor that led to the ending of the series was that Don Johnson wanted out. Johnson was getting tired, and CBS and Paramount had enough episodes to put the series into syndication.


title: Nash Bridges

text: Carlton Cuse went on to become the showrunner for "Lost". "Lost" co-creator Damon Lindelof had started his television writing career on "Nash Bridges". He sought out Cuse's advice on how to run "Lost".


title: Nash Bridges

text: The show has aired in over 70 countries. It currently airs in the Middle East on MBC's newly launched Action block MBC Action, Crime & Investigation Network, WGN America, Universal HD in the United States, TV1 in Australia, 13th Street in The Netherlands and Universal Channel in Serbia and on CBS Action in the United Kingdom. The series currently airs on H&I weekdays at 12pm eastern/11am central.


title: Nash Bridges

text: CBS DVD (distributed by Paramount) released the first three seasons of "Nash Bridges" on DVD in Region 1 in 2008/2009. As of September 2014, these releases have been discontinued and are now out of print.


title: Nash Bridges

text: On September 10, 2014, it was announced that Visual Entertainment (VEI) has sub-licensed the rights to the series from CBS in Region 1 and would release a complete series collection in early 2015. It was subsequently released on November 18, 2014. The 27-disc set contains all 122 episodes of the series. The complete series was reissued by VEI as a 22-disc set in November 2016 to coincide with the anticipated blu-ray release.


title: Nash Bridges

text: On February 10, 2015, VEI released season 4 on DVD as a separate season set. They also re-released the first three seasons on DVD on March 3, 2015.


title: Nash Bridges

text: King Records is releasing all of the seasons on DVD in Region 2, specifically through the Japanese market.


title: Nash Bridges

text: On July 18, 2019, it was reported that USA Network was working with Village Roadshow Entertainment Group, which controlled the Rysher Entertainment intellectual property, to revive "Nash Bridges". The show would reportedly have series star Don Johnson reprising the titular role and serving as one of the showrunners for the project. It was reported to be a two-hour special which, if successful, could serve as a backdoor pilot for a revival of the series. This revival would follow Nash, still running the SFPD's SIU and working to adjust to a new boss and to the changes of San Francisco in the 2020s. In May 2021, further casting for the television film was announced, with series stars Cheech Marin and Jeff Perry reported to return for the film along with Johnson.


title: Nash Bridges

text: The film premiered on November 27, 2021. In January 2022, the revival was nominated for the Outstanding TV Movie at the 33rd GLAAD Media Awards.


title: Mami Wata

text: Mami Wata (Mammy Water), or La Sirene, is a water spirit venerated in West, Central, and Southern Africa and in the African diaspora in the Americas. Mami Wata spirits are usually female but are sometimes male.


title: Mami Wata

text: The appearance of her hair ranges from straight, curly to wooly black and combed straight back. Most scholarly sources suggest the name "Mami Wata" is a pidgin English derivation of "Mother Water", reflecting the goddess's title ("mother of water" or "grandmother of water") in the Agni language of Côte d'Ivoire, although this etymology has been disputed by Africanist writers in favor of various non-English etymologies, for example, the suggestion of a linguistic derivation from ancient Egyptian and Mesopotamian, such as the Egyptian terms ""Mami"" or ""Mama"", meaning "truth" ""Uati"" or ""Uat-Ur"" for "ocean water". While the exact context of the etymology has been challenged, the purpose of Mami Wata's name derived from pidgin English is to both distinguish her "otherness" and connection with the African and African diaspora. Mami Wata is understood to be a foreign spirit by Africans, and the recognition of her and her name is also a recognition of Africans comprehending worlds other than their own.


title: Mami Wata

text: Historical evidence for such deep antiquity of the goddess's tradition has never been offered. Commonly thought to be a single entity, the term has been applied to a number of African water deity traditions across various cultures. These African cultures were often matriarchal and though "Mami Wata" can refer to both male and female deities, they are most typically thought of as feminine and most often take on a female form in artistic representations.


title: Mami Wata

text: Mami Wata is often described as a mermaid-like figure, with a woman's upper body (often nude) and the hindquarters of a fish or serpent. In other tales, Mami Wata is fully human in appearance (though never human). The existence and spiritual importance of Mami Wata is deeply rooted in the ancient tradition and mythology of the coastal southeastern Nigerians (Efik, Ibibio, Igbo, Bahumono and Annang people). Mami Wata often carries expensive baubles such as combs, mirrors, and watches. A large snake (symbol of divination and divinity) frequently accompanies her, wrapping itself around her and laying its head between her breasts. Other times, she may try to pass as completely human, wandering busy markets or patronising bars. She may also manifest in a number of other forms, including as a man. Traders in the 20th century carried similar beliefs with them from Senegal to as far as Zambia. As the Mami Wata traditions continued to re-emerge, native water deities were syncretized into it.


title: Mami Wata

text: While commonly seen with a mirror in hand, Mami Wata is able to embody ritual performances and worship ceremonies for Africans through this instrument. Her mirror represents a movement through the present and the future; her devotees are able to create their own reality through imaging of themselves in their own recreation of Mami Wata's world. In this world, one can embody her sacred powers, fulfilling the inventions of their own reality.


title: Mami Wata

text: Traditions on both sides of the Atlantic tell of the spirit abducting her followers or random people whilst they are swimming or boating. She brings them to her paradisiacal realm, which may be underwater, in the spirit world, or both. Should she allow them to leave, the travellers usually return in dry clothing and with a new spiritual understanding reflected in their gaze. These returnees often grow wealthier, more attractive, and more easygoing after the encounter.


title: Mami Wata

text: Van Stipriaan further reports that other tales describe river travellers (usually men) chancing upon the spirit. She is inevitably grooming herself, combing her hair, and peering at herself in a mirror. Upon noticing the intruder, she flees into the water and leaves her possessions behind. The traveller then takes the invaluable items. Later, Mami Wata appears to the thief in his dreams to demand the return of her things. Should he agree, she further demands a promise from him to be sexually faithful to her. The agreement grants the person riches; refusal to return the possessions or to be faithful brings the man ill-fortune.


title: Mami Wata

text: Her worship is as diverse as her initiates, priesthood and worshippers, although some parallels may be drawn. Groups of people may gather in her name, but the spirit is much more prone to interacting with followers on a one-on-one basis. She thus has many priests and mediums in Africa, America and in the Caribbean who are specifically born and initiated to her.


title: Mami Wata

text: In Nigeria, devotees typically wear red and white clothing, as these colors represent that particular Mami's dual nature. In Igbo iconography, red represents such qualities as death, destruction, heat, being male, physicality, and power. In contrast, white symbolises death, but also can symbolize beauty, creation, being female, new life, spirituality, translucence, water, and wealth. This regalia may also include a cloth snake wrapped about the waist. The Mami Wata shrines may also be decorated in these colors, and items such as bells, carvings, Christian or Indian prints, dolls, incense, spirits, and remnants of previous sacrifices often adorn such places.


title: Mami Wata

text: Intense dancing accompanied by musical instruments such as African guitars or harmonicas often forms the core of Mami Wata worship. Followers dance to the point of entering a trance. At this point, Mami Wata possesses the person and speaks to him or her. Offerings to the spirit are also important, and Mami Wata prefers gifts of delicious food and drink, alcohol, fragrant objects (such as pomade, powder, incense, and soap), and expensive goods like jewellery. Modern worshippers usually leave her gifts of manufactured goods, such as Coca-Cola or designer jewellery.


title: Mami Wata

text: Nevertheless, she largely wants her followers to be healthy and well off. More broadly, people blame the spirit for all sorts of misfortune. In Cameroon, for example, Mami Wata is ascribed with causing the strong undertow that kills many swimmers each year along the coast.


title: Mami Wata

text: According to Bastian, Mami Wata's association with sex and lust is somewhat paradoxically linked to one with . According to a Nigerian tradition, male followers may encounter the spirit in the guise of a beautiful, sexually promiscuous woman, such as a prostitute. In Nigerian popular stories, Mami Wata may seduce a favoured male devotee and then show herself to him following coitus. She then demands his complete sexual faithfulness and secrecy about the matter. Acceptance means wealth and fortune; rejection spells the ruin of his family, finances, and job.


title: Mami Wata

text: Another prominent aspect of the Mami Wata deities is their connection to healing. If someone comes down with an incurable, languorous illness, Mami Wata often takes the blame. The illness is evidence that Mami Wata has taken an interest in the afflicted person and that only she can cure him or her. Similarly, several other ailments may be attributed to the water spirit. In Nigeria, for example, she takes the blame for everything from headaches to sterility.


title: Mami Wata

text: In fact, barren mothers often call upon the spirit to cure their affliction. Many traditions hold that Mami Wata herself is barren, so if she gives a woman a child, that woman inherently becomes more distanced from the spirit's true nature. The woman will thus be less likely to become wealthy or attractive through her devotion to Mami Wata. Images of women with children often decorate shrines to the spirit.


title: Mami Wata

text: The people who inhabit the coastal region from Benin, Ghana and Togo worship a vast pantheon of water deities, of which Mami Wata is most prominent. An entire hierarchy of the Mami Wata priesthood exists in this region to officiate ceremonies, maintain the shrines, conduct healing rituals, and initiate new priests and priestesses into the service of various Mami Wata deities. On February 15, 2020, at 9:00 AM in the city of Cotonou, Benin, Hounnon Behumbeza, a high priest of Vodou and Mami Wata, was officially appointed the Supreme Chief of Mami Wata. As an indication of how revered Mami Wata is in the region, Hounnon Behumbeza's coronation as Supreme Chief of Mami Wata was broadcast live on various television news programs, and featured in local newspapers. The coronation was attended by hundreds of priests from around the region, and the highest dignitaries of Vodou and the Mami Wata tradition. Also in attendance were Benin Republic's minister of culture and several local government officials.


title: Mami Wata

text: Social disparities in West Africa diffused the belief of individual contracts with spirits as the cause of personal wealth and success in earthly life. Mami Wata embodies the power of money, wealth and fame acquired in the absence of ethical laws and obligations to the neighbour. The unique exception is a lifelong contract somewhere read as private investment or as long-term debt that can be extinguished or promised without being fulfilled.


title: Mami Wata

text: As other deities become absorbed into the figure of Mami Wata, the spirit often takes on characteristics unique to a particular region or culture. In Trinidad and Tobago, for example, Maman Dlo plays the role of guardian of nature, punishing overzealous hunters or woodcutters. She is the lover of Papa Bois, a nature spirit.


title: Mami Wata

text: It is believed that all of ancient Africa possessed a multitude of water-spirit traditions before the first contact with Europeans. Most of these were regarded as female. Dual natures of good and evil were not uncommon, reflecting the fact that water is an important means of providing communication, food, drink, trade, and transportation, but it can drown people, flood fields or villages, and provide passage to intruders. Van Stipriaan suggests that she may be based on the West African manatee, which is an idea that has been proposed by scientists of the Ghanaian Council for Scientific and Industrial Research (CSIR); in fact, "Mami Wata" is a common name for this animal in the region. Jill Salmons argues that the mermaid image may have come into being after contact with Europeans. The ships of traders and slavers often had carvings of mermaid figures on their prows, for example, and tales of mermaids were popular among sailors of the time. On the other hand, white is traditionally associated with the spirit world in many cultures of Nigeria. The people of the Cross River area often whiten their skin with talcum or other substances for rituals and for cosmetic reasons, for example.


title: Mami Wata

text: Van Stipriaan speculates that Liberian traders of the Kru ethnic group moved up and down the west coast of Africa from Liberia to Cameroon beginning in the 19th century. They may have spread their own water-spirit beliefs with them and helped to standardise conceptions in West Africa. Their perceived wealth may have helped establish the spirit as one of good fortune.


title: Mami Wata

text: According to Hounnon Behumbeza, high priest of the Mami Wata tradition in West Africa (Benin, Togo and Ghana), "The Mami Wata tradition consists of a huge pantheon of deities and spirits, not just the often portrayed mermaid". Behumbeza goes on to say that "true knowledge and understanding of Mami Wata is shared with those initiated into the priesthood of Mami and with those who hear the calling for initiation into her mysteries."


title: Mami Wata

text: Van Stipriaan also believes that this period introduced West Africa to what would become the definitive image of Mami Wata. Circa 1887, a chromolithograph of a female Samoan snake charmer appeared in Nigeria. According to the British art historian Kenneth C. Murray, the poster was titled "Der Schlangenbändiger" ("The Snake Charmer") and was originally created sometime between 1880 and 1887. Dr. Tobias Wendl, director of the Iwalewa-Haus Africa Centre at the University of Bayreuth, was unable to confirm this after extensive searching (as "Der Schlangenbändiger" is a masculine term, the title seems suspect). He did discover a very similar photograph titled "Die samoanische Schlangenbändigerin Maladamatjaute" ("the Samoan Snake Charmer (fem.) Maladamatjaute") in the collection of the Wilhelm-Zimmermann Archive in Hamburg. Whichever the original image, it was almost certainly a poster of a celebrated late 19th-century snake charmer who performed under the stage name "Nala Damajanti", which appeared in several variations, particularly "Maladamatjaute", at numerous venues, including the Folies Bergère in 1886. This identification was also made by Drewal in a 2012 book chapter on Mami Wata. Despite exotic claims of her nationality, she was later identified as one Émilie Poupon of Nantey, France.


title: Mami Wata

text: This image—an enticing woman with long, black hair and a large snake slithering up between her breasts, ambiguous if she is human or mermaid beyond the image—apparently caught the imaginations of the Africans who saw it; it was the definitive image of the spirit. Before long, Mami Wata posters appeared in over a dozen countries and the popular image was reproduced in 1955 by the Shree Ram Calendar Company in Bombay for the African market. People began creating Mami Wata art of their own, much of it influenced by the lithograph.


title: Mami Wata

text: According to photographer Van Stipriaan and some western anthropologists, the various West African religions came to resemble one another during the 20th century, especially in urban areas. The homogenisation was largely the result of greater communication and mobility of individuals from town to town and country to country, though links between the spirit's nature and the perils of the urban environment have also been proposed. This led to a new level of standardisation of priests, initiations of new devotees, healing rituals, and temples.


title: Mami Wata

text: The 20th century also led to Mami Wata's reemergence in much of Central and Southern Africa. In the mid-1950s, traders imported copies of "The Snake Charmer" from Bombay and England and sold them throughout Africa. West African traders moved her to Lubumbashi in the Democratic Republic of the Congo (DRC) in that same decade. There the spirit became a popular subject of Congolese folk painters, who placed her on the walls of bars, stores, and marketplace stalls. Senegalese traders and Congolese immigrants probably brought her worship to Zambia by the 1970s. Meanwhile, Congolese and Zambian artists spread Mami Wata images throughout public places in Zambia. Further diffusion might have occurred during the Biafran secessionist Nigerian Civil War, which began in 1967. Refugees fled to all parts of West and Central Africa, bringing with them their belief in the water spirit.


title: Mami Wata

text: Modern DRC, Lesotho, South Africa, and Zambia today form the current boundary of the Mami Wata cult, albeit a blurred one. The pan-African water spirit is assimilating native water spirits in this region, many of them serpent figures. Some examples are the Congolese-Zambian "chitapo" or "nakamwale", the South African "umamlambo", and the Sotho "mamolapo" or "mamogashoa". The most visible evidence of this absorption is that many of these creatures are today viewed as mermaids rather than snakes, their traditional form. These adoptions often lead to confusion when aspects of more than one being become amalgamated under the name "Mami Wata". In Southern Africa, for example, Mami Wata is sometimes said to be able to fly around in the form of a tornado, an adopted aspect from the "khanyapa" water spirit.


title: Mami Wata

text: The new environment only served to emphasize the enslaved's connection to water. In Guiana, for example, slaves had to fight back swamp waters on the plantations they worked. She was first mentioned in Dutch Guiana in the 1740s in the journal of an anonymous colonist:


title: Mami Wata

text: Slaves worshipped the spirit by dancing and then falling into a trancelike state. In the 1770s, the Dutch rulers outlawed the ritual dances associated with the spirit. The governor, J. Nepveu, wrote that


title: Mami Wata

text: Native Americans of the colony adopted Watermama from the slaves and merged her with their own water spirits.


title: Mami Wata

text: By the 19th century, an influx of enslaved Africans from other regions had relegated Watermama to a position in the pantheon of the deities of the Surinamese Winti religion. When Winti was outlawed in the 1970s, her religious practices lost some of their importance in Suriname. Furthermore, a relative lack of freedom compared to their African brethren prevented the homogenisation that occurred with the Mami Wata cult across the Atlantic.


title: Mami Wata

text: In Haiti, Lasirenn is a Vodou loa who represents Mami Wata. She is described as a strong-willed, sensual siren who possesses the ability to drown those enticed by her. Lasirenn is often depicted as a half-fish, half-human being, but is occasionally portrayed as a whale. Similar to many other depictions of Mami Wata, Lasirenn is often shown gazing at herself in a mirror, a symbolic representation of her beauty. She is often associated with queer relationships among Black women.


title: Mami Wata

text: Mami Wata is a popular subject in the art, fiction, poetry, music, and film of the Caribbean and West and Central Africa. Visual artists especially seem drawn to her image, and both wealthier Africans and tourists buy paintings and wooden sculptures of the spirit. She also figures prominently in the folk art of Africa, with her image adorning walls of bars and living rooms, album covers, and other items.


title: Mami Wata

text: Mami Wata has also proved to be a popular theme in African and Caribbean literature. Authors who have featured her in their fiction include Wayne Gerard Trotman as Mama Dlo in his novel "Kaya Abaniah and the Father of the Forest", Patrick Chamoiseau, Alex Godard, Rose Marie Guiraud (Côte d'Ivoire), Flora Nwapa, and Véronique Tadjo (Côte d'Ivoire). "Mamy-Wata" is also the title of a satirical Cameroonian newspaper.


title: Mami Wata

text: The character Mami Watanabe from the comic book "Factionalists" is the physical manifestation of the spirit entity Mami Wata. The author utilized a number of features to convey this. Her name Mami Watanabe is a play on Mami Wata. Despite being Japanese, her skin is darkened in the Japanese ganguro style. She also has a tattoo of a snake on her body and receives a watch and a mirror as gifts in the series, two items generally associated with Mami Wata.


title: Mami Wata

text: Singer-songwriter S.J. Tucker recorded a song named "La Sirene" in honor of Mami Watanabe. Trumpeter Hugh Masekela recorded a song titled "Mami Wata", which appears on the CD version of his album "The Boy's Doin' It".


title: Mami Wata

text: Mami Wata appeared in the second season of the Canadian television show "Lost Girl" on Showcase Television. She is also referred to in the television show "River Monsters" while Jeremy Wade is fishing in the Congo River in the episode "Congo Killer". She is referred to again in the "Body Snatcher" episode set in Guyana. In this second episode, Wade speculates that legends of Mami Wata in Guyana could have originated by Arapaima attacks.


title: Mami Wata

text: Lasiren is a key figure in Canadian-Jamaican writer Nalo Hopkinson's 2003 erotic historical fiction novel "The Salt Roads".


title: Mami Wata

text: In Nigerian-American author Nnedi Okorafor's 2014 speculative fiction novel "Lagoon", an alien spaceship appears beneath the waters of Lagos Lagoon and the new arrivals cause transformations in the natural and human world. When the first alien ambassador sets foot on the Bar Beach in human female form, then disappears into the sea, a local boy compares her to Mami Wata. Later, an antagonist interprets another alien in female form as Mami Wata and surrenders to her seduction, accompanying her into the sea to be transformed.


title: Mami Wata

text: Mami Wata is a pivotal character in the second and third books in the Tristan Strong series by author Kwame Mbalia.


title: Mami Wata

text: In the 2021 novel, Skin of the Sea by Nigerian-Welsh writer Natasha Bowen, Mami Wata is one of the seven creatures created by Yemoja to collect the soul of the dead enslaved Africans and the lead character Simi is a Mami Wata.


title: Mami Wata

text: In 2022, the feature film, Nanny, written and directed by Nikyatu Jusu, portraits the figure of Mami Wata in relation to the main character Aisha, a Senegalese woman living in the US. The film won Best Jury Prize at the Sundance 2022 Film Festival. It was subsequently acquired by Amazon Studios and Blumhouse and opened in the U.S. on November 23, 2022. and on Amazon Prime on December 16, 2022


title: Credit Karma

text: Credit Karma is an American multinational personal finance company founded in 2007, which has been a brand of Intuit since December 2020. It is best known as a free credit and financial management platform, but its features also include monitoring of unclaimed property databases and a tool to identify and dispute credit report errors. The company operates in the United States, Canada and the United Kingdom.


title: Credit Karma

text: All of Credit Karma’s services are free to consumers. Revenue from targeted advertisements for financial products offsets the costs of its free products and services. Credit Karma earns revenue from lenders, who pay the company when Credit Karma successfully recommends customers to the lenders.


title: Credit Karma

text: Kenneth Lin, who previously founded Multilytics Marketing and worked with E-Loan and Upromise, launched Credit Karma in 2007 with co-founders Ryan Graciano and Nichole Mustard. The website went live in February 2008. Early investors included Chris Larson, CEO of Prosper, and Mark Lefanowicz, former president of E-Loan.


title: Credit Karma

text: In November 2009, Credit Karma closed a $2.5 million Series A funding round led by QED Investors with participation from SV Angel, Felicis Ventures and Founders Fund. In 2013, Credit Karma secured $30 million in Series B funding led by Ribbit Capital and Susquehanna Growth Equity.


title: Credit Karma

text: In March 2014, Credit Karma raised $85 million in Series C financing, led by CapitalG with participation from Tiger Global Management and existing investors. The company followed that with $75 million in follow on funding in September 2014 from CapitalG, Tiger Global Management and Susquehanna Growth Equity.


title: Credit Karma

text: In December 2015, Credit Karma acquired mobile notifications app developer Snowball for an undisclosed amount. As of 2015, Credit Karma had raised $368.5 million in financing, at a valuation of $3.5 billion.


title: Credit Karma

text: In 2016, Credit Karma acquired money reclamation service Claimdog. In December 2016, Credit Karma acquired AFJC Corporation, owner of OnePriceTaxes.com, to accelerate its entry into the tax preparation market. Related to the launch of tax preparation services, the company increased its workforce and opened offices in Los Angeles and Charlotte, North Carolina.


title: Credit Karma

text: In May 2017, Credit Karma launched Unclaimed Money in seven US states. The product aims to help users find unclaimed money, such as unclaimed refunds and insurance payouts.


title: Credit Karma

text: In March 2018, Credit Karma acquired personal finance company Penny for an undisclosed amount. In August, it acquired mortgage platform Approved for an undisclosed amount.


title: Credit Karma

text: In May 2019, the customers of the Noddle credit reporting service in the United Kingdom were acquired from TransUnion.


title: Credit Karma

text: In December 2020, Intuit acquired Credit Karma for approximately $7.1 billion. The acquisition was initially delayed due to a DOJ antitrust lawsuit but it was finally approved after the company agreed to divest its free tax preparation service, known as Credit Karma Tax, which was a direct competitor to Intuit's TurboTax product.


title: Credit Karma

text: In August 2021, Credit Karma reached an agreement with NBA franchise Houston Rockets to have the company’s name appear on the team’s jersey’s beginning in the 2021 season.


title: Credit Karma

text: In September 2022, the Federal Trade Commission (FTC) ordered Credit Karma to pay its users $3million for "false claims" that impacted their credit scores. Nearly one-thirds of pre-approved users who applied for credit cards were eventually denied following a credit check, costing their time and a negative impact to their credit score. Credit Karma reached a settlement with the FTC, and stated that the company is paid only when users are approved for products like credit cards.


title: Credit Karma

text: Credit Karma provides free credit scores and credit reports in the United States, Canada and United Kingdom from national credit bureaus TransUnion and Equifax, alongside daily credit monitoring from TransUnion.


title: Credit Karma

text: Credit Karma also provides identity theft protection and credit tools, such as a Credit Score Simulator which simulates the effect of potential financial actions on a user's credit score; and tailored recommendations for credit cards and personal loans.


title: Credit Karma

text: Credit Karma Tax, its free United States tax filing service, was announced in December 2016. Credit Karma Tax does not participate in the Free File Alliance, and so is not bound by its requirements to restrict eligibility for free filing. The company's primary competitors in this area are TaxAct, TurboTax and H&R Block. In November 2020, Square, Inc. announced it was acquiring Credit Karma Tax for $50 million and would make it a part of its Cash App unit.


title: Man-of-war

text: The man-of-war (also man-o'-war, or simply man) was a Royal Navy expression for a powerful warship or frigate from the 16th to the 19th century. Although the term never acquired a specific meaning, it was usually reserved for a ship armed with cannon and propelled primarily by sails, as opposed to a galley which is propelled primarily by oars.


title: Man-of-war

text: The man-of-war was developed in Portugal in the early 15th century from earlier roundships with the addition of a second mast to form the carrack. The 16th century saw the carrack evolve into the galleon and then the ship of the line. The evolution of the term has been given thus:


title: Man-of-war

text: The man-of-war design developed by Sir John Hawkins had three masts, each with three to four sails. The ship could be up to 60 metres long and could have up to 124 guns: four at the bow, eight at the stern, and 56 in each broadside. All these cannons required three gun decks to hold them, one more than any earlier ship. It had a maximum sailing speed of eight or nine knots.


title: Özge Yağız

text: Özge Yağız was born on 26 September 1997 in Istanbul. She acquired her education from Başkent University in Communication Sciences Academy. She started her acting career in 2018, with a small role in season 3 of the series "Adını Sen Koy" and portrayed the character of Zeliha, which was broadcast on Star TV. In February 2019, she appeared in the series "Yemin" on Kanal 7, and depicted the character of Reyhan, it was her first leading role. Later in 2020, she starred in "Sol Yanım" and portrayed the character of Serra, which was broadcast on Star TV. It starred Tolga Mendi, Cemre Baysel and Cansel Elçin.


title: Özge Yağız

text: In 2020, she was transferred to the historical fiction series "" and it was decided that she will depict the character of Malhun Hatun, wife of Osman I, however this thought was later dropped and actress Yıldız Çağrı Atiksoy depicted the character of Malhun.


title: Özge Yağız

text: In 2021, she began working on the series "İçimizden Biri" in which she depicted the character of Havva, daughter of a Turkish Muslim family, who falls in love with Adam, son of an Irish Christian family.


title: Octal

text: The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. This is to say that 10 represents eight and 100 represents sixty-four. However, English, like most languages, uses a base-10 number system, hence a true octal system might use different vocabulary.


title: Octal

text: By performing the calculation above in the familiar decimal system, we see why 112 in octal is equal to formula_3 in decimal.


title: Octal

text: Octal numerals can be easily converted from binary representations (similar to a quaternary numeral system) by grouping consecutive binary digits into groups of three (starting from the right, for integers). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: , corresponding to the octal digits , yielding the octal representation 112.


title: Octal

text: Gottfried Wilhelm Leibniz made the connection between trigrams, hexagrams and binary numbers in 1703.


title: Octal

text: Octal became widely used in computing when systems such as the UNIVAC 1050, PDP-8, ICL 1900 and IBM mainframes employed 6-bit, 12-bit, 24-bit or 36-bit words. Octal was an ideal abbreviation of binary for these machines because their word size is divisible by three (each octal digit represents three binary digits). So two, four, eight or twelve digits could concisely display an entire machine word. It also cut costs by allowing Nixie tubes, seven-segment displays, and calculators to be used for the operator consoles, where binary displays were too complex to use, decimal displays needed complex hardware to convert radices, and hexadecimal displays needed to display more numerals.


title: Octal

text: All modern computing platforms, however, use 16-, 32-, or 64-bit words, further divided into eight-bit bytes. On such systems three octal digits per byte would be required, with the most significant octal digit representing two binary digits (plus one bit of the next significant byte, if any). Octal representation of a 16-bit word requires 6 digits, but the most significant octal digit represents (quite inelegantly) only one bit (0 or 1). This representation offers no way to easily read the most significant byte, because it's smeared over four octal digits. Therefore, hexadecimal is more commonly used in programming languages today, since two hexadecimal digits exactly specify one byte. Some platforms with a power-of-two word size still have instruction subwords that are more easily understood if displayed in octal; this includes the PDP-11 and Motorola 68000 family. The modern-day ubiquitous x86 architecture belongs to this category as well, but octal is rarely used on this platform, although certain properties of the binary encoding of opcodes become more readily apparent when displayed in octal, e.g. the ModRM byte, which is divided into fields of 2, 3, and 3 bits, so octal can be useful in describing these encodings. Before the availability of assemblers, some programmers would handcode programs in octal; for instance, Dick Whipple and John Arnold wrote Tiny BASIC Extended directly in machine code, using octal.


title: Octal

text: Octal is sometimes used in computing instead of hexadecimal, perhaps most often in modern times in conjunction with file permissions under Unix systems (see chmod). It has the advantage of not requiring any extra symbols as digits (the hexadecimal system is base-16 and therefore needs six additional symbols beyond 0–9). It is also used for digital displays.


title: Octal

text: In programming languages, octal literals are typically identified with a variety of prefixes, including the digit codice_1, the letters codice_2 or codice_3, the digit–letter combination codice_4, or the symbol codice_5 or codice_6. In "Motorola convention", octal numbers are prefixed with codice_7, whereas a small (or capital) letter codice_2 or codice_3 is added as a postfix following the "Intel convention". In Concurrent DOS, Multiuser DOS and REAL/32 as well as in DOS Plus and DR-DOS various environment variables like $CLS, $ON, $OFF, $HEADER or $FOOTER support an codice_10 octal number notation, and DR-DOS DEBUG utilizes codice_11 to prefix octal numbers as well.


title: Octal

text: For example, the literal 73 (base 8) might be represented as codice_12, codice_13, codice_14, codice_15, codice_16, codice_17, codice_18, codice_19 or codice_20 in various languages.


title: Octal

text: Newer languages have been abandoning the prefix codice_1, as decimal numbers are often represented with leading zeroes. The prefix codice_3 was introduced to avoid the prefix codice_2 being mistaken for a zero, while the prefix codice_4 was introduced to avoid starting a numerical literal with an alphabetic character (like codice_2 or codice_3), since these might cause the literal to be confused with a variable name. The prefix codice_4 also follows the model set by the prefix codice_28 used for hexadecimal literals in the C language; it is supported by Haskell, OCaml, Python as of version 3.0, Raku, Ruby, Tcl as of version 9, PHP as of version 8.1, Rust and it is intended to be supported by ECMAScript 6 (the prefix codice_1 originally stood for base 8 in JavaScript but could cause confusion, therefore it has been discouraged in ECMAScript 3 and dropped in ECMAScript 5).


title: Octal

text: Octal numbers that are used in some programming languages (C, Perl, PostScript...) for textual/graphical representations of byte strings when some byte values (unrepresented in a code page, non-graphical, having special meaning in current context or otherwise undesired) have to be to escaped as codice_10. Octal representation may be particularly handy with non-ASCII bytes of UTF-8, which encodes groups of 6 bits, and where any start byte has octal value codice_31 and any continuation byte has octal value codice_32.


title: Octal

text: Octal was also used for floating point in the Ferranti Atlas (1962), Burroughs B5500 (1964), Burroughs B5700 (1971), Burroughs B6700 (1971) and Burroughs B7700 (1972) computers.


title: Octal

text: Transponders in aircraft transmit a "squawk" code, expressed as a four-octal-digit number, when interrogated by ground radar. This code is used to distinguish different aircraft on the radar screen.


title: Octal

text: To convert integer decimals to octal, divide the original number by the largest possible power of 8 and divide the remainders by successively smaller powers of 8 until the power is 1. The octal representation is formed by the quotients, written in the order generated by the algorithm.


title: Octal

text: To convert a decimal fraction to octal, multiply by 8; the integer part of the result is the first digit of the octal fraction. Repeat the process with the fractional part of the result, until it is null or within acceptable error bounds.


title: Octal

text: These two methods can be combined to handle decimal numbers with both integer and fractional parts, using the first on the integer part and the second on the fractional part.


title: Octal

text: To convert integer decimals to octal, prefix the number with "0.". Perform the following steps for as long as digits remain on the right side of the radix:


title: Octal

text: Double the value to the left side of the radix, using "octal" rules, move the radix point one digit rightward, and then place the doubled value underneath the current value so that the radix points align. If the moved radix point crosses over a digit that is 8 or 9, convert it to 0 or 1 and add the carry to the next leftward digit of the current value. "Add" "octally" those digits to the left of the radix and simply drop down those digits to the right, without modification.


title: Octal

text: In this formula, is an individual octal digit being converted, where is the position of the digit (counting from 0 for the right-most digit).


title: Octal

text: For double-digit octal numbers this method amounts to multiplying the lead digit by 8 and adding the second digit to get the total.


title: Octal

text: To convert octals to decimals, prefix the number with "0.". Perform the following steps for as long as digits remain on the right side of the radix: Double the value to the left side of the radix, using "decimal" rules, move the radix point one digit rightward, and then place the doubled value underneath the current value so that the radix points align. "Subtract" "decimally" those digits to the left of the radix and simply drop down those digits to the right, without modification.


title: Octal

text: The process is the reverse of the previous algorithm. The binary digits are grouped by threes, starting from the least significant bit and proceeding to the left and to the right. Add leading zeroes (or trailing zeroes to the right of decimal point) to fill out the last group of three if necessary. Then replace each trio with the equivalent octal digit.


title: Octal

text: The conversion is made in two steps using binary as an intermediate base. Octal is converted to binary and then binary to hexadecimal, grouping digits by fours, which correspond each to a hexadecimal digit.


title: Octal

text: Hexadecimal to octal conversion proceeds by first converting the hexadecimal digits to 4-bit binary values, then regrouping the binary bits into 3-bit octal digits.


title: Octal

text: Due to having only factors of two, many octal fractions have repeating digits, although these tend to be fairly simple:


title: Mission to Mars

text: Mission to Mars is a 2000 American science fiction adventure film directed by Brian De Palma, written by Jim Thomas, John Thomas, and Graham Yost, and suggested by Disney's theme park attraction of the same name. The film depicts the first crewed Mars exploration mission going awry; American astronaut Jim McConnell (Gary Sinise) helps to coordinate a rescue mission for a colleague. Principal support actors were Tim Robbins, Don Cheadle, Connie Nielsen, Jerry O'Connell, and Kim Delaney.


title: Mission to Mars

text: In 2020, the "Mars I" mission launches for planet Mars, commanded by Luke Graham (Don Cheadle). Upon arrival, the team discovers a bright white formation in the Cydonia region, which they suspect is an extrusion from a subsurface geothermal column of water, useful to future human colonization. After reporting this to the Earth-orbiting World Space Station, they go to investigate the formation and start hearing a low sound on their communications system. Radar initially reports that the formation is metal, but when they increase power to the radar, a large vortex appears and kills everyone except Luke. After the vortex subsides, the formation is revealed to be part of a large humanoid face.


title: Mission to Mars

text: The event creates an electromagnetic pulse the space station observes, after which it receives a distress message from Luke. Realizing Luke couldn't have left because the pulse would have damaged the computer system of the ERV ("Earth Return Vehicle"), they repurpose the "Mars II" mission into a rescue.


title: Mission to Mars

text: Months later, as "Mars Rescue", consisting of Commander Woody Blake (Tim Robbins), his wife Terri Fisher (Connie Nielsen), recent widower Jim McConnell (Gary Sinise), and technician Phil Ohlmyer (Jerry O'Connell), nears Mars orbit, they discover that all satellite imagery of the formation area is covered with static. Micrometeoroids breach the ship, causing damage to the external fuel lines and resulting in the engines exploding. With the destroyed Mars II out of control, crew are forced to abandon ship and travel in their spacesuits to the REMO ("Resupply Module") in a nearby orbit over Mars. Woody launches himself at the module and manages to attach a tether to it, but loses his grip and begins descending into the Martian atmosphere. Terri attempts to rescue Woody, but knowing she would run out of fuel before reaching him, Woody removes his helmet, killing himself to save her.


title: Mission to Mars

text: The survivors arrive on the Martian surface, and begin repairing the ERV. They find Luke living in a greenhouse; he shows them pictures of the face, and reveals that the pulses in the low sound they heard represented a 3D model of human-like DNA, but missing a pair of chromosomes. Jim determines they must complete the sequence to pass a test, and they send a rover to broadcast the completed signal via radar. Following the transmission, an opening appears in the side of the structure. With a massive dust storm approaching Jim, Terri, and Luke head to the formation, while Phil stays to finish repairing the ERV. Phil is ordered to launch, with or without them, before the storm hits.


title: Mission to Mars

text: The three astronauts enter the opening, which seals behind them. A three-dimensional projection of the solar system depicts the planet Mars, covered with water, being struck by a large asteroid and rendered uninhabitable. A projection of a humanoid Martian lifeform reveals that the native Martians evacuated the planet in spaceships, one of which was sent to seed Earth with DNA, intending to create life that could one day land on Mars and be recognized as descendants. An invitation is offered for one of their group to follow the Martians to their new home. Jim accepts the invitation, bidding farewell to Terri and Luke, and is sealed inside a small capsule. Terri and Luke race back to the ERV and arrive just as Phil is about to take off. They barely escape the dust storm into space as Jim's capsule is launched from the crumbling formation and past them toward the Martians' home.


title: Mission to Mars

text: The film was shot primarily on location in Vancouver, British Columbia; Jordan; and the Canary Islands. Extensive special effects surrounding certain aspects of the film such as the NASA spacecraft and Martian vortex, were created by a number of digital effects companies including ILM, Dream Quest Images, Tippett Studio, CIS Hollywood, and Trans FX. Between visuals, miniatures, and animation, over 400 technicians were directly involved in the production aspects of the special effects.


title: Mission to Mars

text: According to the director in the 2015 documentary film about his career, De Palma was brought on board after the previous director walked away due to concerns over the lack of additional money for the budget. De Palma indicated that the film needed additional funds and that much of the budget went into the CGI for the film. When De Palma was hired the script had already been written and the film cast.


title: Mission to Mars

text: The original score for "Mission to Mars", was released by the Hollywood Records music label on March 14, 2000. The score for the film was composed by Ennio Morricone and performed by the New York Philharmonic. Suzana Peric and Nick Meyers edited the film's music.


title: Mission to Mars

text: The film, produced by Disney's Touchstone Pictures, was distributed by Buena Vista Pictures in North America, and Spyglass Entertainment in selected European territories. "Mission to Mars" explores astronomy, extraterrestrial life, and space exploration. Despite the fact that the film employed the use of numerous extensive special effects, it failed to garner any award nominations from mainstream motion picture organizations for its production merits. On March 14, 2000, the original film score was released by the Hollywood Records label. It was composed, orchestrated, and conducted by Italian composer Ennio Morricone.


title: Mission to Mars

text: Among mainstream critics in the U.S., the film received mainly negative reviews. Rotten Tomatoes reported that 25% of 110 sampled critics gave the film a positive review, with an average score of 4.1/10 and the consensus, "Beauty only goes skin deep in this shallow but visually stunning film." At Metacritic, which assigns a weighted average out of 100 to critics' reviews, the film received a score of 34 based on 36 reviews. Furthermore, the film was nominated for a Golden Raspberry Award for Brian De Palma in the category of 'Worst Director', where he lost to Roger Christian for "Battlefield Earth". Audiences surveyed by CinemaScore gave the film a grade "C−" on scale of A to F. On the Taste of Cinema website, David Harkin felt that Mission to Mars was an "enjoyable slice of sci-fi, with [director De Palma's] trademark mix of stylish camera movements and visual flourishes".


title: Mission to Mars

text: The film's reception among French-language critics was markedly different in positive fashion. Film journal "Cahiers du cinéma" devoted several articles to De Palma and "Mission to Mars" at the time of its release, and placed it as "#4" in their list of the "10 best films of 2000". The film was screened out of competition at the 2000 Cannes Film Festival.