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Programming languages should allow a user to specify a minimum precision for intermediate calculations of expressions for each radix. Interchange formats are intended for the exchange of floating-point data using a fixed-length bit-string for a given format.
For decimal floating point, there are additional exceptions along with the above: The Wikibook Floating Point has a page on the topic of: Missing functions tanPi, asinPi and acosPi”. For numbers with an exponent in the normal range the exponent field being not all ones or all zerosthe leading bit of the significand will always be 1.
The standard also defines interchange formatswhich generalize these basic formats. For instance, if binary32 is the largest supported binary format, then a conversion from a decimal external sequence with 12 decimal digits is guaranteed to be correctly rounded when converted to binary32; but conversion of a sequence of 13 decimal digits is not; however the standard recommends that implementations impose no such limit.
Retrieved 6 August List of International Electrotechnical Commission standards. This rule allows the binary format to have an extra bit of precision.
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The binary formats in the original standard are included in the new standard along with three new basic formats, one binary and two decimal. The following table summarizes the smallest interchange formats including the basic ones. A format may also include how the set is encoded.
IEEE has strengthened up many of these, but a few variations still remain especially for binary formats. The traps and other exception mechanisms remain optional, as they were in IEEE P P P P P For the exchange of decimal floating-point numbers, interchange formats of any multiple of 32 bits are defined.
Clause 9 in the standard recommends fifty operations, that language standards should define. Some numbers may have several possible exponential format representations. The encoding scheme for these binary interchange formats is the same as that of IEEE The predicate ie with the normal comparison operations when they say one floating point number is less than another.
The standard addressed many problems found in the diverse floating point implementations that made them difficult to use reliably and portably.
Such a figure can be ice to select iex appropriate format given the expected value of a number and the required precision. The standard recommends that languages provide a method of specifying p and emax for each supported base b. The standard requires operations to convert between basic formats and external character sequence formats. The IEEE allowed many variations in implementations such as the encoding of some values and the detection of certain exceptions.
Interchange is complicated by the fact that some external indicator of the representation in use is required. The former is more convenient for direct hardware implementation of the standard, while the latter is more suited to software emulation on a binary computer. The operations also include setting and accessing uec mode rounding direction,  and implementation-defined vector reduction operations such as sum, scaled product, and dot productwhose accuracy is unspecified by the standard.
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754–1 So for instance a bit extended precision binary number must have an ’emax’ of at least The standard does not require an implementation to support extended or extendable precision formats. This is referred to as “preferredWidth” in the 754-11, and it should be possible to set this on a per block basis. Views Read Edit View history. The original binary value will be preserved by converting to decimal and back again using: The standard recommends that languages and implementations support an extended format which has a greater precision than the largest basic format supported for each radix b.
An extendable precision format allows the user to specify the precision and exponent range.
Intermediate calculations within expressions should be calculated, and any temporaries saved, using the maximum of the width of the operands and the preferred width, if set. The standard provides a predicate totalOrder which defines a total ordering for all floating point data for each format.
Retrieved March 28, To conform to the current standard, an implementation must implement at least one of the basic formats as both an arithmetic format and an interchange format. Many hardware floating point units now use the IEEE standard.