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BER: variable-length big-endian binary representation (up to 2 2 1024 bits); PER Unaligned: a fixed number of bits if the integer type has a finite range; a variable number of bits otherwise; PER Aligned: a fixed number of bits if the integer type has a finite range and the size of the range is less than 65536; a variable number of octets ...
For example, 32 contiguous bits may be treated as an array of 32 Booleans, a 4-byte string, an unsigned 32-bit integer or an IEEE single precision floating point value. Because the stored bits are never changed, the programmer must know low level details such as representation format, byte order, and alignment needs, to meaningfully cast.
A less trivial example is representing a sorted list by a sorted array, which allows search in logarithmic time by binary search. Contrast with a search tree, specifically a binary search tree, which also allows logarithmic-time search, but requires pointers. A sorted array is only efficient as a static data structure, as modifying the list is ...
The exponent field is an 11-bit unsigned integer from 0 to 2047, in biased form: an exponent value of 1023 represents the actual zero. Exponents range from −1022 to +1023 because exponents of −1023 (all 0s) and +1024 (all 1s) are reserved for special numbers.
For example, to perform an element by element sum of two arrays, a and b to produce a third c, it is only necessary to write c = a + b In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine.
With the example in view, a number of details can be discussed. The most important is the choice of the representation of the big number. In this case, only integer values are required for digits, so an array of fixed-width integers is adequate. It is convenient to have successive elements of the array represent higher powers of the base.
The array, set and dictionary binary types are made up of pointers - the objref and keyref entries - that index into an object table in the file. This means that binary plists can capture the fact that - for example - a separate array and dictionary serialized into a file both have the same data element stored in them.
Concise Binary Object Representation (CBOR) is a binary data serialization format loosely based on JSON authored by Carsten Bormann and Paul Hoffman. [a] Like JSON it allows the transmission of data objects that contain name–value pairs, but in a more concise manner. This increases processing and transfer speeds at the cost of human readability.