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80-467: One of the series was also known as the APE(X)C or All Purpose Electronic X-Ray Computer and was sited at Birkbeck. From 1943 on, Booth started working on the determination of crystal structures using X-ray diffraction data. The computations involved were extremely tedious and there was ample incentive for automating the process. He developed an analogue computer to compute the reciprocal spacings of

160-930: A grain boundary . Like a grain boundary, a twin boundary has different crystal orientations on its two sides. But unlike a grain boundary, the orientations are not random, but related in a specific, mirror-image way. Mosaicity is a spread of crystal plane orientations. A mosaic crystal consists of smaller crystalline units that are somewhat misaligned with respect to each other. In general, solids can be held together by various types of chemical bonds , such as metallic bonds , ionic bonds , covalent bonds , van der Waals bonds , and others. None of these are necessarily crystalline or non-crystalline. However, there are some general trends as follows: Metals crystallize rapidly and are almost always polycrystalline, though there are exceptions like amorphous metal and single-crystal metals. The latter are grown synthetically, for example, fighter-jet turbines are typically made by first growing

240-515: A molten condition nor entirely in solution, but the high temperature and pressure conditions of metamorphism have acted on them by erasing their original structures and inducing recrystallization in the solid state. Other rock crystals have formed out of precipitation from fluids, commonly water, to form druses or quartz veins. Evaporites such as halite , gypsum and some limestones have been deposited from aqueous solution, mostly owing to evaporation in arid climates. Water-based ice in

320-619: A molten fluid, or by crystallization out of a solution. Some ionic compounds can be very hard, such as oxides like aluminium oxide found in many gemstones such as ruby and synthetic sapphire . Covalently bonded solids (sometimes called covalent network solids ) are typically formed from one or more non-metals, such as carbon or silicon and oxygen, and are often very hard, rigid, and brittle. These are also very common, notable examples being diamond and quartz respectively. Weak van der Waals forces also help hold together certain crystals, such as crystalline molecular solids , as well as

400-416: A "crystal" is based on the microscopic arrangement of atoms inside it, called the crystal structure . A crystal is a solid where the atoms form a periodic arrangement. ( Quasicrystals are an exception, see below ). Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a polycrystalline structure. In

480-410: A 32-bit accumulator and a 32-bit data register (used along with the 32-bit accumulator to implement 64-bit shift instructions and hold the 64-bit result of a multiplication ). Instructions and data are stored in two magnetic drums , for a total of 32 circular magnetic tracks of 32 words. Since the rotation rate is 3750 rpm (62.5 rotations per second), the program execution speed can go from as high as

560-504: A four-bit opcode can specify up to sixteen different ALU operations. Generally, an ALU opcode is not the same as a machine language instruction , though in some cases it may be directly encoded as a bit field within such instructions. The status outputs are various individual signals that convey supplemental information about the result of the current ALU operation. General-purpose ALUs commonly have status signals such as: The status inputs allow additional information to be made available to

640-555: A fraction of a millimetre to several centimetres across, although exceptionally large crystals are occasionally found. As of 1999 , the world's largest known naturally occurring crystal is a crystal of beryl from Malakialina, Madagascar , 18 m (59 ft) long and 3.5 m (11 ft) in diameter, and weighing 380,000 kg (840,000 lb). Some crystals have formed by magmatic and metamorphic processes, giving origin to large masses of crystalline rock . The vast majority of igneous rocks are formed from molten magma and

720-473: A paper tape reader, and a paper tape puncher. The puncher output could be fed to a printer ('teletyper') unit when desirable. Printer output is emulated and is displayed on screen. Tape input was either computer-generated by the APEXC, or hand-typed with a special 32-key keyboard (each tape row had 5 data holes (<-> bits), which makes 32 different values). Crystal A crystal or crystalline solid

800-608: A perfect, exactly repeating pattern. However, in reality, most crystalline materials have a variety of crystallographic defects : places where the crystal's pattern is interrupted. The types and structures of these defects may have a profound effect on the properties of the materials. A few examples of crystallographic defects include vacancy defects (an empty space where an atom should fit), interstitial defects (an extra atom squeezed in where it does not fit), and dislocations (see figure at right). Dislocations are especially important in materials science , because they help determine

880-434: A single crystal of titanium alloy, increasing its strength and melting point over polycrystalline titanium. A small piece of metal may naturally form into a single crystal, such as Type 2 telluric iron , but larger pieces generally do not unless extremely slow cooling occurs. For example, iron meteorites are often composed of single crystal, or many large crystals that may be several meters in size, due to very slow cooling in

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960-721: A single solid. Polycrystals include most metals , rocks, ceramics , and ice . A third category of solids is amorphous solids , where the atoms have no periodic structure whatsoever. Examples of amorphous solids include glass , wax , and many plastics . Despite the name, lead crystal, crystal glass , and related products are not crystals, but rather types of glass, i.e. amorphous solids. Crystals, or crystalline solids, are often used in pseudoscientific practices such as crystal therapy , and, along with gemstones , are sometimes associated with spellwork in Wiccan beliefs and related religious movements. The scientific definition of

1040-585: A very simple 8-bit ALU: Mathematician John von Neumann proposed the ALU concept in 1945 in a report on the foundations for a new computer called the EDVAC . The cost, size, and power consumption of electronic circuitry was relatively high throughout the infancy of the Information Age . Consequently, all early computers had a serial ALU that operated on one data bit at a time although they often presented

1120-435: A wide range of properties. Polyamorphism is a similar phenomenon where the same atoms can exist in more than one amorphous solid form. Crystallization is the process of forming a crystalline structure from a fluid or from materials dissolved in a fluid. (More rarely, crystals may be deposited directly from gas; see: epitaxy and frost .) Crystallization is a complex and extensively-studied field, because depending on

1200-601: A wider word size to programmers. The first computer to have multiple parallel discrete single-bit ALU circuits was the 1951 Whirlwind I , which employed sixteen such "math units" to enable it to operate on 16-bit words. In 1967, Fairchild introduced the first ALU-like device implemented as an integrated circuit, the Fairchild 3800, consisting of an eight-bit arithmetic unit with accumulator. It only supported adds and subtracts but no logic functions. Full integrated-circuit ALUs soon emerged, including four-bit ALUs such as

1280-424: Is a solid material whose constituents (such as atoms , molecules , or ions ) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape , consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation

1360-445: Is a noncrystalline form. Polymorphs, despite having the same atoms, may have very different properties. For example, diamond is the hardest substance known, while graphite is so soft that it is used as a lubricant. Chocolate can form six different types of crystals, but only one has the suitable hardness and melting point for candy bars and confections. Polymorphism in steel is responsible for its ability to be heat treated , giving it

1440-436: Is an algorithm that operates on integers which are larger than the ALU word size. To do this, the algorithm treats each integer as an ordered collection of ALU-size fragments, arranged from most-significant (MS) to least-significant (LS) or vice versa. For example, in the case of an 8-bit ALU, the 24-bit integer 0x123456 would be treated as a collection of three 8-bit fragments: 0x12 (MS), 0x34 , and 0x56 (LS). Since

1520-451: Is believed that no executive or operating system was ever written for the APEXC, although there were subroutine libraries of sorts for common arithmetic, I/O and debug tasks. Operation of the machine is normally done through a control panel which allows the user to start, stop and resume the central processing unit , and to alter registers and memory when the CPU is stopped. When starting

1600-493: Is decomposed into 32 1-bit memory and arithmetic operations: this takes 32 bit cycles, for a total of 1 word cycle. The processor is fairly efficient: most instructions take only 2 word cycles (1 for fetch, 1 for read operand and execute), with the exception of stores, shifts and multiplications. The APEXC CPU qualifies as RISC ; there is no other adequate word. Note there is no read-only memory (ROM), and therefore no bootstrap loader or default start-up program whatsoever. It

1680-580: Is impossible for an ordinary periodic crystal (see crystallographic restriction theorem ). The International Union of Crystallography has redefined the term "crystal" to include both ordinary periodic crystals and quasicrystals ("any solid having an essentially discrete diffraction diagram" ). Quasicrystals, first discovered in 1982, are quite rare in practice. Only about 100 solids are known to form quasicrystals, compared to about 400,000 periodic crystals known in 2004. The 2011 Nobel Prize in Chemistry

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1760-415: Is in contrast to a floating-point unit (FPU), which operates on floating point numbers. It is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs). The inputs to an ALU are the data to be operated on, called operands , and a code indicating the operation to be performed; the ALU's output

1840-483: Is its visible external shape. This is determined by the crystal structure (which restricts the possible facet orientations), the specific crystal chemistry and bonding (which may favor some facet types over others), and the conditions under which the crystal formed. By volume and weight, the largest concentrations of crystals in the Earth are part of its solid bedrock . Crystals found in rocks typically range in size from

1920-589: Is known as crystallography . The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification . The word crystal derives from the Ancient Greek word κρύσταλλος ( krustallos ), meaning both " ice " and " rock crystal ", from κρύος ( kruos ), "icy cold, frost". Examples of large crystals include snowflakes , diamonds , and table salt . Most inorganic solids are not crystals but polycrystals , i.e. many microscopic crystals fused together into

2000-415: Is made of 15 instructions only, namely addition , subtraction , multiplication, load (3 variants), store (2 variants), conditional branch , right arithmetic bit shift, right bit rotation, punched-card input, punched-card output, machine stop, and bank-switching (which is never used on the APEXC, since it only has 1024 words of storage, and addresses are 10-bit-long). A so-called vector mode enables to repeat

2080-473: Is mechanically very strong, the sheets are rather loosely bound to each other. Therefore, the mechanical strength of the material is quite different depending on the direction of stress. Not all crystals have all of these properties. Conversely, these properties are not quite exclusive to crystals. They can appear in glasses or polycrystals that have been made anisotropic by working or stress —for example, stress-induced birefringence . Crystallography

2160-460: Is operating, external circuits apply signals to the ALU inputs and, in response, the ALU produces and conveys signals to external circuitry via its outputs. A basic ALU has three parallel data buses consisting of two input operands ( A and B ) and a result output ( Y ). Each data bus is a group of signals that conveys one binary integer number. Typically, the A, B and Y bus widths (the number of signals comprising each bus) are identical and match

2240-410: Is referred to as the "status register" or "condition code register". Depending on the ALU operation being performed, some status register bits may be changed and others may be left unmodified. For example, in bitwise logical operations such as AND and OR, the carry status bit is typically not modified as it is not relevant to such operations. In CPUs, the stored carry-out signal is usually connected to

2320-407: Is repeated for all operand fragments so as to generate a complete collection of partials, which is the result of the multiple-precision operation. In arithmetic operations (e.g., addition, subtraction), the algorithm starts by invoking an ALU operation on the operands' LS fragments, thereby producing both a LS partial and a carry out bit. The algorithm writes the partial to designated storage, whereas

2400-425: Is the result of the performed operation. In many designs, the ALU also has status inputs or outputs, or both, which convey information about a previous operation or the current operation, respectively, between the ALU and external status registers . An ALU has a variety of input and output nets , which are the electrical conductors used to convey digital signals between the ALU and external circuitry. When an ALU

2480-471: Is the science of measuring the crystal structure (in other words, the atomic arrangement) of a crystal. One widely used crystallography technique is X-ray diffraction . Large numbers of known crystal structures are stored in crystallographic databases . Arithmetic logic unit In computing , an arithmetic logic unit ( ALU ) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers . This

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2560-424: Is the type of impurities present in a corundum crystal. In semiconductors , a special type of impurity, called a dopant , drastically changes the crystal's electrical properties. Semiconductor devices , such as transistors , are made possible largely by putting different semiconductor dopants into different places, in specific patterns. Twinning is a phenomenon somewhere between a crystallographic defect and

2640-466: The Am2901 and 74181 . These devices were typically " bit slice " capable, meaning they had "carry look ahead" signals that facilitated the use of multiple interconnected ALU chips to create an ALU with a wider word size. These devices quickly became popular and were widely used in bit-slice minicomputers. Microprocessors began to appear in the early 1970s. Even though transistors had become smaller, there

2720-447: The mechanical strength of materials . Another common type of crystallographic defect is an impurity , meaning that the "wrong" type of atom is present in a crystal. For example, a perfect crystal of diamond would only contain carbon atoms, but a real crystal might perhaps contain a few boron atoms as well. These boron impurities change the diamond's color to slightly blue. Likewise, the only difference between ruby and sapphire

2800-430: The ALU inputs. Typically, the external circuitry employs sequential logic to generate the signals that control ALU operation. The external sequential logic is paced by a clock signal of sufficiently low frequency to ensure enough time for the ALU outputs to settle under worst-case conditions (i.e., conditions resulting in the maximum possible propagation delay). For example, a CPU starts an addition operation by routing

2880-414: The ALU when performing an operation. Typically, this is a single "carry-in" bit that is the stored carry-out from a previous ALU operation. An ALU is a combinational logic circuit, meaning that its outputs will change asynchronously in response to input changes. In normal operation, stable signals are applied to all of the ALU inputs and, when enough time (known as the " propagation delay ") has passed for

2960-400: The ALU's carry-in net. This facilitates efficient propagation of carries (which may represent addition carries, subtraction borrows, or shift overflows) when performing multiple-precision operations, as it eliminates the need for software-management of carry propagation (via conditional branching, based on the carry status bit). In integer arithmetic computations, multiple-precision arithmetic

3040-481: The APE(X)C (All-Purpose Electronic Computer) series. The computers were programmed by Kathleen. The APE(X)C series included the following machines: Only one of each of these machines was built, with the exception of HEC (and possibly MAC) which were commercial machines produced in quite large numbers for the time, around 150. They were similar in design, with various small differences, mostly in I/O equipment. The APEHC

3120-696: The Hollerith Electronic Computer 1 (HEC 1) before the end of 1951. The computer was a direct copy of Andrew Booth's circuits with extra Input/output interfaces. The HEC 2 was the HEC 1 with smarter metal casings and was built for the Business Efficiency Exhibition in 1953. A slightly modified version of the HEC 2 was then marketed as HEC2M and 8 were sold. The HEC2M was succeeded by the HEC4. Around 100 HEC4s were sold in

3200-518: The LS bit of each partial—which is conveyed via the stored carry bit—must be obtained from the MS bit of the previously left-shifted, less-significant operand. Conversely, operands are processed MS first in right-shift operations because the MS bit of each partial must be obtained from the LS bit of the previously right-shifted, more-significant operand. In bitwise logical operations (e.g., logical AND, logical OR),

3280-429: The air ( ice fog ) more often grow from a supersaturated gaseous-solution of water vapor and air, when the temperature of the air drops below its dew point , without passing through a liquid state. Another unusual property of water is that it expands rather than contracts when it crystallizes. Many living organisms are able to produce crystals grown from an aqueous solution , for example calcite and aragonite in

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3360-510: The case of most molluscs or hydroxylapatite in the case of bones and teeth in vertebrates . The same group of atoms can often solidify in many different ways. Polymorphism is the ability of a solid to exist in more than one crystal form. For example, water ice is ordinarily found in the hexagonal form Ice I h , but can also exist as the cubic Ice I c , the rhombohedral ice II , and many other forms. The different polymorphs are usually called different phases . In addition,

3440-404: The conditions, a single fluid can solidify into many different possible forms. It can form a single crystal , perhaps with various possible phases , stoichiometries , impurities, defects , and habits . Or, it can form a polycrystal , with various possibilities for the size, arrangement, orientation, and phase of its grains. The final form of the solid is determined by the conditions under which

3520-409: The crystal can shrink or stretch it. Another is birefringence , where a double image appears when looking through a crystal. Moreover, various properties of a crystal, including electrical conductivity , electrical permittivity , and Young's modulus , may be different in different directions in a crystal. For example, graphite crystals consist of a stack of sheets, and although each individual sheet

3600-411: The crystal is one grain in a polycrystalline solid. The flat faces (also called facets ) of a euhedral crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal : they are planes of relatively low Miller index . This occurs because some surface orientations are more stable than others (lower surface energy ). As a crystal grows, new atoms attach easily to

3680-532: The crystals may form hexagons, such as ordinary water ice ). Crystals are commonly recognized, macroscopically, by their shape, consisting of flat faces with sharp angles. These shape characteristics are not necessary for a crystal—a crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape—but the characteristic macroscopic shape is often present and easy to see. Euhedral crystals are those that have obvious, well-formed flat faces. Anhedral crystals do not, usually because

3760-606: The degree of crystallization depends primarily on the conditions under which they solidified. Such rocks as granite , which have cooled very slowly and under great pressures, have completely crystallized; but many kinds of lava were poured out at the surface and cooled very rapidly, and in this latter group a small amount of amorphous or glassy matter is common. Other crystalline rocks, the metamorphic rocks such as marbles , mica-schists and quartzites , are recrystallized. This means that they were at first fragmental rocks like limestone , shale and sandstone and have never been in

3840-517: The diffraction pattern. In 1947, along with his collaborator and future spouse Kathleen Britten , he spent a few months with von Neumann 's team, which was the leading edge in computer research at the time. Booth designed an electromechanical computer, the ARC (Automatic Relay Computer), in the late 1940s (1947-1948). Later on, they built an experimental electronic computer named SEC ( Simple Electronic Computer , designed around 1948-1949) - and finally,

3920-453: The eight faces of the octahedron belong to another crystallographic form reflecting a different symmetry of the isometric system. A crystallographic form is described by placing the Miller indices of one of its faces within brackets. For example, the octahedral form is written as {111}, and the other faces in the form are implied by the symmetry of the crystal. Forms may be closed, meaning that

4000-710: The final block of ice, each of the small crystals (called " crystallites " or "grains") is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does not have a periodic arrangement of atoms, because the periodic pattern is broken at the grain boundaries . Most macroscopic inorganic solids are polycrystalline, including almost all metals , ceramics , ice , rocks , etc. Solids that are neither crystalline nor polycrystalline, such as glass , are called amorphous solids , also called glassy , vitreous, or noncrystalline. These have no periodic order, even microscopically. There are distinct differences between crystalline solids and amorphous solids: most notably,

4080-531: The fluid is being solidified, such as the chemistry of the fluid, the ambient pressure , the temperature , and the speed with which all these parameters are changing. Specific industrial techniques to produce large single crystals (called boules ) include the Czochralski process and the Bridgman technique . Other less exotic methods of crystallization may be used, depending on the physical properties of

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4160-415: The form can completely enclose a volume of space, or open, meaning that it cannot. The cubic and octahedral forms are examples of closed forms. All the forms of the isometric system are closed, while all the forms of the monoclinic and triclinic crystal systems are open. A crystal's faces may all belong to the same closed form, or they may be a combination of multiple open or closed forms. A crystal's habit

4240-402: The form of snow , sea ice , and glaciers are common crystalline/polycrystalline structures on Earth and other planets. A single snowflake is a single crystal or a collection of crystals, while an ice cube is a polycrystal . Ice crystals may form from cooling liquid water below its freezing point, such as ice cubes or a frozen lake. Frost , snowflakes, or small ice crystals suspended in

4320-458: The interlayer bonding in graphite . Substances such as fats , lipids and wax form molecular bonds because the large molecules do not pack as tightly as atomic bonds. This leads to crystals that are much softer and more easily pulled apart or broken. Common examples include chocolates, candles, or viruses. Water ice and dry ice are examples of other materials with molecular bonding. Polymer materials generally will form crystalline regions, but

4400-526: The late 1950s. The HEC used standard punched cards ; the HEC 4 had a printer, too, and it featured several instructions (such as divide ) and registers not found on the APEXC. An emulator for the APEXC series has been developed by MESS . They describe its functioning as follows: The APEXC is an incredibly simple machine. Instruction and data words are always 32 bits long. The processor uses integer arithmetic with 2's complement representation. Addresses are 10 bits long. The APEXC has no RAM , except for

4480-471: The lengths of the molecules usually prevent complete crystallization—and sometimes polymers are completely amorphous. A quasicrystal consists of arrays of atoms that are ordered but not strictly periodic. They have many attributes in common with ordinary crystals, such as displaying a discrete pattern in x-ray diffraction , and the ability to form shapes with smooth, flat faces. Quasicrystals are most famous for their ability to show five-fold symmetry, which

4560-470: The machine, the address of the first instruction of the program to be executed must be entered in the control panel, then the run switch must be pressed. Most programs end with a stop instruction, which enables the operator to check the state of the machine, possibly run some post-mortem debugging procedures (a core dump routine is described in an APEXC programming book), then enter the address of another program and run it. Two I/O devices were supported:

4640-427: The native word size of the external circuitry (e.g., the encapsulating CPU or other processor). The opcode input is a parallel bus that conveys to the ALU an operation selection code, which is an enumerated value that specifies the desired arithmetic or logic operation to be performed by the ALU. The opcode size (its bus width) determines the maximum number of distinct operations the ALU can perform; for example,

4720-567: The next clock, are allowed to propagate through the ALU and to the destination register while the CPU waits for the next clock. When the next clock arrives, the destination register stores the ALU result and, since the ALU operation has completed, the ALU inputs may be set up for the next ALU operation. A number of basic arithmetic and bitwise logic functions are commonly supported by ALUs. Basic, general purpose ALUs typically include these operations in their repertoires: ALU shift operations cause operand A (or B) to shift left or right (depending on

4800-406: The opcode) and the shifted operand appears at Y. Simple ALUs typically can shift the operand by only one bit position, whereas more complex ALUs employ barrel shifters that allow them to shift the operand by an arbitrary number of bits in one operation. In all single-bit shift operations, the bit shifted out of the operand appears on carry-out; the value of the bit shifted into the operand depends on

4880-588: The operand fragments may be processed in any arbitrary order because each partial depends only on the corresponding operand fragments (the stored carry bit from the previous ALU operation is ignored). Although it is possible to design ALUs that can perform complex functions, this is usually impractical due to the resulting increases in circuit complexity, power consumption, propagation delay, cost and size. Consequently, ALUs are typically limited to simple functions that can be executed at very high speeds (i.e., very short propagation delays), with more complex functions being

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4960-422: The operands from their sources (typically processor registers ) to the ALU's operand inputs, while simultaneously applying a value to the ALU's opcode input that configures it to perform an addition operation. At the same time, the CPU enables the destination register to store the ALU output (the resulting sum from the addition operation) upon operation completion. The ALU's input signals, which are held stable until

5040-410: The partial is written to designated storage. This process repeats until all operand fragments have been processed, resulting in a complete collection of partials in storage, which comprise the multi-precision arithmetic result. In multiple-precision shift operations, the order of operand fragment processing depends on the shift direction. In left-shift operations, fragments are processed LS first because

5120-413: The process of forming a glass does not release the latent heat of fusion , but forming a crystal does. A crystal structure (an arrangement of atoms in a crystal) is characterized by its unit cell , a small imaginary box containing one or more atoms in a specific spatial arrangement. The unit cells are stacked in three-dimensional space to form the crystal. The symmetry of a crystal is constrained by

5200-415: The processor's state machine typically stores the carry out bit to an ALU status register. The algorithm then advances to the next fragment of each operand's collection and invokes an ALU operation on these fragments along with the stored carry bit from the previous ALU operation, thus producing another (more significant) partial and a carry out bit. As before, the carry bit is stored to the status register and

5280-432: The requirement that the unit cells stack perfectly with no gaps. There are 219 possible crystal symmetries (230 is commonly cited, but this treats chiral equivalents as separate entities), called crystallographic space groups . These are grouped into 7 crystal systems , such as cubic crystal system (where the crystals may form cubes or rectangular boxes, such as halite shown at right) or hexagonal crystal system (where

5360-455: The responsibility of external circuitry. For example: An ALU is usually implemented either as a stand-alone integrated circuit (IC), such as the 74181 , or as part of a more complex IC. In the latter case, an ALU is typically instantiated by synthesizing it from a description written in VHDL , Verilog or some other hardware description language . For example, the following VHDL code describes

5440-423: The rougher and less stable parts of the surface, but less easily to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. (See diagram on right.) One of the oldest techniques in the science of crystallography consists of measuring the three-dimensional orientations of the faces of a crystal, and using them to infer

5520-444: The same atoms may be able to form noncrystalline phases . For example, water can also form amorphous ice , while SiO 2 can form both fused silica (an amorphous glass) and quartz (a crystal). Likewise, if a substance can form crystals, it can also form polycrystals. For pure chemical elements, polymorphism is known as allotropy . For example, diamond and graphite are two crystalline forms of carbon , while amorphous carbon

5600-451: The same operation 32 times with 32 successive memory locations. Note the lack of bitwise and/or/xor and division. Also, note the lack of indirect addressing modes: dynamic modification of opcodes is the only way one may simulate it. Another oddity is that the memory bus and the ALU are 1-bit-wide. There is a 64 kHz bit-clock and a 2 kHz word-clock, and each word memory and arithmetic operation

5680-437: The signals to propagate through the ALU circuitry, the result of the ALU operation appears at the ALU outputs. The external circuitry connected to the ALU is responsible for ensuring the stability of ALU input signals throughout the operation, and for allowing sufficient time for the signals to propagate through the ALU circuitry before sampling the ALU outputs. In general, external circuitry controls an ALU by applying signals to

5760-432: The size of a fragment exactly matches the ALU word size, the ALU can directly operate on this "piece" of operand. The algorithm uses the ALU to directly operate on particular operand fragments and thus generate a corresponding fragment (a "partial") of the multi-precision result. Each partial, when generated, is written to an associated region of storage that has been designated for the multiple-precision result. This process

5840-744: The substance, including hydrothermal synthesis , sublimation , or simply solvent-based crystallization . Large single crystals can be created by geological processes. For example, selenite crystals in excess of 10  m are found in the Cave of the Crystals in Naica, Mexico. For more details on geological crystal formation, see above . Crystals can also be formed by biological processes, see above . Conversely, some organisms have special techniques to prevent crystallization from occurring, such as antifreeze proteins . An ideal crystal has every atom in

5920-417: The theoretical maximum of 1 kIPS to lower than 100IPS if program instructions and data are not contiguous. Nowadays, many say a pocket calculator is faster. One oddity is that there is no program counter : each machine instruction includes the address of the next instruction. This design may sound weird, but it is the only way to achieve optimal performance with this cylinder-based memory. The machine code

6000-404: The type of shift. Upon completion of each ALU operation, the ALU's status output signals are usually stored in external registers to make them available for future ALU operations (e.g., to implement multiple-precision arithmetic ) and for controlling conditional branching . The bit registers that store the status output signals are often collectively treated as a single, multi-bit register, which

6080-429: The underlying crystal symmetry . A crystal's crystallographic forms are sets of possible faces of the crystal that are related by one of the symmetries of the crystal. For example, crystals of galena often take the shape of cubes, and the six faces of the cube belong to a crystallographic form that displays one of the symmetries of the isometric crystal system . Galena also sometimes crystallizes as octahedrons, and

6160-620: The vacuum of space. The slow cooling may allow the precipitation of a separate phase within the crystal lattice, which form at specific angles determined by the lattice, called Widmanstatten patterns . Ionic compounds typically form when a metal reacts with a non-metal, such as sodium with chlorine. These often form substances called salts, such as sodium chloride (table salt) or potassium nitrate ( saltpeter ), with crystals that are often brittle and cleave relatively easily. Ionic materials are usually crystalline or polycrystalline. In practice, large salt crystals can be created by solidification of

6240-668: Was a punched card machine while the APEXC, APERC and APENC were teletypers ( keyboard and printer , plus paper tape reader and puncher). Also, the UCC had 8k words of storage, instead of 1k word for other machines, and the MAC used germanium diodes in replacement of many valves. In March 1951, the British Tabulating Machine Company (BTM) sent a team to Andrew Booth's workshop. They then used his design to create

6320-400: Was awarded to Dan Shechtman for the discovery of quasicrystals. Crystals can have certain special electrical, optical, and mechanical properties that glass and polycrystals normally cannot. These properties are related to the anisotropy of the crystal, i.e. the lack of rotational symmetry in its atomic arrangement. One such property is the piezoelectric effect , where a voltage across

6400-530: Was sometimes insufficient die space for a full-word-width ALU and, as a result, some early microprocessors employed a narrow ALU that required multiple cycles per machine language instruction. Examples of this includes the popular Zilog Z80 , which performed eight-bit additions with a four-bit ALU. Over time, transistor geometries shrank further, following Moore's law , and it became feasible to build wider ALUs on microprocessors. Modern integrated circuit (IC) transistors are orders of magnitude smaller than those of

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