Decimal Cases * * * () * () In programming, a floating point number is expressed as . In general, a floating-point number can be written as
where * M is the fraction mantissa or significand. * E is the exponent. * B is the base, in decimal case . Binary Cases As an example, a 32-bit word is used in MIPS computer to represent a floating-point number: 1 bit ..... 8 bits .............. 23 bits representing: * The implied base is 2 (not explicitly shown in the representation). * The exponent can be represented in signed 2's complement (but also see biased notation later). * The implied decimal point is between the exponent field E and the significand field M. * More bits in field E mean larger range of values representable. * More bits in field M mean higher precision. * Zero is represented by all bits equal to 0: Normalization To efficiently use the bits available for the significand, it is shifted to the left until all leading 0's disappear (as they make no contribution to the precision). The value can be kept unchanged by adjusting the exponent accordingly. Moreover, as the MSB of the significand is always 1, it does not need to be shown explicitly. The significand could be further shifted to the left by 1 bit to gain one more bit for precision. The first bit 1 before the decimal point is implicit. The actual value represented is
However, to avoid possible confusion, in the following the default normalization does not assume this implicit 1 unless otherwise specified. Zero is represented by all 0's and is not (and cannot be) normalized. Example: A binary number can be represented in 14-bit floating-point form in the following ways (1 sign bit, a 4-bit exponent field and a 9-bit significand field): * * * * * with an implied 1.0: By normalization, highest precision can be achieved. The bias depends on number of bits in the exponent field. If there are e bits in this field, the bias is , which lifts the representation (not the actual exponent) by half of the range to get rid of the negative parts represented by 2's complement. The range of actual exponents represented is still the same. With the biased exponent, the value represented by the notation is:
Note: * Zero exponent is represented by , the bias of the notation; * The range of exponents representable is from -126 to 127; * The exponent (with all zero significand) is reserved to represent infinities or not-a-number (NaN) which may occur when, e.g., a number is divided by zero; * The smallest exponent is reserved to represent denormalized numbers (smaller than which cannot be normalized) and zero, e.g., is represented by: Normalization: If the implied base is , the significand must be shifted multiple of q bits at a time so that the exponent can be correspondingly adjusted to keep the value unchanged. If at least one of the first q bits of the significand is 1, the representation is normalized. Obviously, the implied 1 can no longer be used. Examples: * Normalize . Note that the base is 4 (instead of 2)
Note that the significand has to be shifted to the left twobits at a time during normalization, because the smallest reduction of the exponent necessary to keep the value represented unchanged is 1, corresponding to dividing the value by 4. Similarly, if the implied base is , the significand has to be shifted 3 bits at a time. In general, if , normalization means to left shift the significand q bits at a time until there is at least one 1 in the highest q bits of the significand. Obviously the implied 1 can not be used. * Represent in biased notation with bits for exponent field. The bias is and implied base is 2.
The biased exponent is , and the notation is (without implied 1): or (with implied 1): * Find the value represented in this biased notation: The biased exponent is 17, the actual exponent is , the value is (without implied 1):
or (with implied 1):
Examples of IEEE 754: * -0.3125
The biased exponent is , * 1.0
The biased exponent is , * 37.5
The based exponent: , . * -78.25
The biased exponent: , * As the most negative exponent representable is -126, this value is a denorm which cannot be normalized: by GAURAV PANDEY & VIJAY MAHARA..........
Of course computers are important in advertising! you wouldn't be able to make advertisments if you didn't have computers. A lot of ads have computer generated effects or animation, this wouldn't be able to be done without computers.
Processing data is the manipulation of data so as to generate meaningful information. This is commonly done using computers.
The meaning of computer science is the study of science done through computers. It is using procedures and algorithms to study data and computer systems.
A server is nothing more than a computer that that is being used to distribute computer files (or other types of information) on demand to other computers. Once a server is enabled (which can be done on most computers if they have the requisite software) the computer waits for requests from remote computers (called clients), finds the requested files or data in its system, processes it if necessary, and then sends it to the remote computer.
There are many advantages to using computers. Some of these include storage, ease of transmission, ease of social contact, and getting tasks done more efficiently.
In a decimal floating point number representation it is always possible to use a power of 10 (exponent) to write a number so that it lies between 0 and 1, by changing the exponent. For example: 5 = 0.5 x 10 50 = 0.5 x (10 to the power 2) 0.05 = 0.5 x (10 to the power -1) This is called normalisation. In the binary representation of floating point numbers it is always possible to shift the number until it starts with a 1, provided you change the exponent at the same time. This is how computer memory works. If you do this, however, the 1 does not need to be stored (because it can always be added with a little extra processing). So in computers the number is often normalised, and the leading 1 omitted. But if the storage convention assumes this is done, then, of course, it must be done for every number stored in memory.
An arithmetic-logic unit (ALU) is the part of a computer processor (CPU) that carries out arithmetic and logic operations on the operands in computer instruction words. In some processors, the ALU is divided into two units, an arithmetic unit (AU) and a logic unit (LU). Some processors contain more than one AU - for example, one for fixed-point operations and another for floating-point operations. (In personal computers floating point operations are sometimes done by a floating point unit on a separate chip called a numeric coprocessor.)
Not a Number or NaN is a special case coded value in IEEE floating point, which most computers now use by default. It basically means that a calculation was done with invalid operands (e.g. 0/0, log(0), square root of a negative number).The main advantage of NaN for computers, especially those with deeply pipelined floating point arithmetic units, is it eliminates large numbers of floating point exceptions causing pipeline flushes... allowing the error to propagate to the end of the calculation and be detected by a simple test for NaN instead of having to handle an exception and all its overhead. This allows both for significant speed increase and in some computers simpler circuitry.Another special case coded value in IEEE floating pointis Infinity or Inf. It basically means what it says and results from calculations that overflow (e.g. divide by zero).
A method for storing and calculating numbers in which the decimal points do not line up as in fixed point numbers. The significant digits are stored as a unit called the "mantissa," and the location of the radix point (decimal point in base 10) is stored in a separate unit called the "exponent." Floating point methods are used for calculating a large range of numbers quickly. Floating point operations can be implemented in hardware (math coprocessor), or they can be done in software. In large systems, they can also be performed in a separate floating point processor that is connected to the main processor via a channel.
If you are referring to normalization of floating point numbers, it is to maintain the most precision of the number possible. Leading zeros in floating point representation is lost precision, thus normalization removes the leading zeros by shifting left and adjusting the exponent. If the calculation was done in a hidden extended precision register (like IEEE 80-bit format) extra precision bits may be shifted in to the LSBs before restoring the result to a standard single or double precision register, reducing loss of precision.
practicly anything nowadays with vista and advanced computers
There are many tasks that computers do that had to be done by hand before the existence of computers. Tasks such as file keeping, writing, and record keeping all used to be done by hand at home and at one's job.
A collective representation of ones work which he/she has done towards better public representation of self.
Everything. All that is done with computers requires software.
What Can Be Done at This Point was created in 2007.
Vicarious representation refers to acting that is done on behalf on another person. This may be through actions or feelings of another person.