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Binary Angular Measurement
Binary angular measurement (BAM) (and the binary angular measurement system, BAMS) is a measure of angles using binary numbers and fixed-point arithmetic, in which a full turn (angle), turn is represented by the value 1. The unit of measure, unit of angular measure used in those methods may be called binary radian (brad) or binary degree. These representation of angles are often used in numerical control and digital signal processing applications, such as robotics, navigation, computer games, and digital sensors, taking advantage of the implicit modular reduction achieved by truncating binary numbers. It may also be used as the fractional part of a fixed-point number counting the number of full rotations of e.g. a vehicle's wheels or a leadscrew. Representation Unsigned fraction of turn In this system, an angle is represented by an ''n''-bit unsigned binary number in the sequence 0, ..., 2''n''−1 that is interpreted as a multiple of 1/2''n'' of a full turn; that is, 360/2''n'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. More generally angles are also formed wherever two lines, rays or line segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides. Angles can also be formed by the intersection of two planes or by two intersecting curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term ''angle'' is also used for the size, magnitude (mathematics), magnitude or Physical quantity, quantity of these types of geometric figures and in this context an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two's Complement
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the ''greatest'' value as the ''sign'' to indicate whether the binary number is positive or negative; when the most significant bit is ''1'' the number is signed as negative and when the most significant bit is ''0'' the number is signed as positive. As a result, non-negative numbers are represented as themselves: 6 is 0110, zero is 0000, and −6 is 1010 (the result of applying the bitwise NOT operator to 6 and adding 1). However, while the number of binary bits is fixed throughout a computation it is otherwise arbitrary. Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero. Furthermore, arithmetic implementations can be used on signed as well as unsigned integers and differ only in the integer overflow situations. Proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Polygon
In mathematics, a constructible polygon is a regular polygon that can be Compass and straightedge constructions, constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with an odd number of sides are known. Conditions for constructibility Some regular polygons are easy to construct with compass and straightedge; others are not. The Greek mathematics, ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, and they knew how to construct a regular polygon with double the number of sides of a given regular polygon.Bold, Benjamin. ''Famous Problems of Geometry and How to Solve Them'', Dover Publications, 1982 (orig. 1969). This led to the question being posed: is it possible to construct ''all'' regular polygons with compass and straightedge? If not, which ''n''-gons (that is, polygons wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CORDIC
CORDIC, short for coordinate rotation digital computer, is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, and exponentials and logarithms In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ... with arbitrary base, typically converging with one digit (or bit) per iteration. CORDIC is therefore also an example of digit-by-digit algorithms. The original system is sometimes referred to as Volder's algorithm. CORDIC and closely related methods known as pseudo-multiplication and pseudo-division or factor combining are commonly used when no hardware multiplier is available (e.g. in simple microcontrollers and field-programmable gate arrays or FPGAs), as the only operations they require are addition, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Scaling
In computing, fixed-point is a method of representing fraction (mathematics), fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. US dollar, Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cent (currency), cents (1/100 of dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals. Fixed-point number representation is often contrasted to the more complicated and computationally demanding floating-point representation. In the fixed-point representation, the fraction is often expressed in the same number base as the integer part, but using negative exponentiation, powers of the base ''b''. The most common variants are decimal (base 10) and binary number, binary (base 2). The latter is commonly known also as binary scaling. Thus, if ''n'' fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grade (angle)
In trigonometry, the gradianalso known as the gon (), grad, or gradeis a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees. It is equivalent to of a turn, of a degree, or of a radian. Measuring angles in gradians (gons) is said to employ the ''centesimal'' system of angular measurement, initiated as part of metrication and decimalisation efforts. In continental Europe, the French word ''centigrade'', also known as ''centesimal minute of arc'', was in use for one hundredth of a grade; similarly, the ''centesimal second of arc'' was defined as one hundredth of a centesimal arc-minute, analogous to decimal time and the sexagesimal minutes and seconds of arc. The chance of confusion was one reason for the adoption of the term '' Celsius'' to replace ''centigrade'' as the name of the temperature scale. Gradians (gons) are principally used in surveying (especially in Europe), and to a less ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GPS Signals
GPS signals are broadcast by Global Positioning System satellites to enable satellite navigation. Using these signals, receivers on or near the Earth's surface can determine their Position, Velocity and Time (PVT). The GPS satellite constellation is operated by the 2nd Space Operations Squadron (2SOPS) of Space Delta 8, United States Space Force. GPS signals include ranging signals, which are used to measure the distance to the satellite, and navigation messages. The navigation messages include ephemeris data which are used both in trilateration to calculate the position of each satellite in orbit and also to provide information about the time and status of the entire satellite constellation, called the almanac. There are four GPS signal specifications designed for civilian use. In order of date of introduction, these are: L1 C/A, L2C, L5 and L1C. L1 C/A is also called the ''legacy signal'' and is broadcast by all currently operational satellites. L2C, L5 and L1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes are commonly used in astronomy and orbital mechanics. A real orbit and its elements change over time due to gravitational Perturbation (astronomy), perturbations by other objects and the effects of general relativity. A Kepler orbit is an idealized, mathematical approximation of the orbit at a particular time. When viewed from an inertial frame, two orbiting bodies trace out distinct trajectories. Each of these trajectories has its Focus (geometry), focus at the common center of mass. When viewed from a non-inertial frame centered on one of the bodies, only the trajectory of the opposite body is apparent; Keplerian elements describe these non-inertial trajectories. An orbit has two sets of Keplerian elements depe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ephemeris
In astronomy and celestial navigation, an ephemeris (; ; , ) is a book with tables that gives the trajectory of naturally occurring astronomical objects and artificial satellites in the sky, i.e., the position (and possibly velocity) over time. Historically, positions were given as printed tables of values, given at regular intervals of date and time. The calculation of these tables was one of the first applications of mechanical computers. Modern ephemerides are often provided in electronic form. However, printed ephemerides are still produced, as they are useful when computational devices are not available. The astronomical position calculated from an ephemeris is often given in the spherical polar coordinate system of right ascension and declination, together with the distance from the origin if applicable. Some of the astronomical phenomena of interest to astronomers are eclipses, apparent retrograde motion/planetary stations, planetary es, sidereal time, positions for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Positioning System
The Global Positioning System (GPS) is a satellite-based hyperbolic navigation system owned by the United States Space Force and operated by Mission Delta 31. It is one of the global navigation satellite systems (GNSS) that provide geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. It does not require the user to transmit any data, and operates independently of any telephone or Internet reception, though these technologies can enhance the usefulness of the GPS positioning information. It provides critical positioning capabilities to military, civil, and commercial users around the world. Although the United States government created, controls, and maintains the GPS system, it is freely accessible to anyone with a GPS receiver. Overview The GPS project was started by the U.S. Department of Defense in 1973. The first prototype spacecraft was launched in 1978 an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometric Functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis. The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their multiplicative inverse, reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric functions has a corresponding Inverse trigonometric functions, inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related to right-an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
