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Densely packed decimal (DPD) is an efficient method for binary encoding decimal digits.. The traditional system of binary encoding for decimal digits, known as binary-coded decimal (BCD), uses four bits to encode each digit, resulting in significant wastage of binary data bandwidth (since four bits can store 16 states and are being used to store only 10), even when using packed BCD.
Reversible Implementation of Densely-Packed-Decimal Converter to and from Binary-Coded-Decimal Format Using in IEEE-754R. 9th International Conference on Information Technology (ICIT'06). IEEE. pp. 273–276. Cowlishaw, Mike F. (2009) [2002, 2008]. "Bibliography of material on Decimal Arithmetic – by category". General Decimal Arithmetic. IBM
BCD numbers can be represented in two ways in integer registers: packed decimal and unpacked decimal. Packed (4 bits) In packed decimal representation a decimal digit is stored in one nibble. The values 10 to 15 are not used. [2] Unpacked (8 bits) In unpacked decimal representation a decimal digit is stored in one byte. The values 10 to 255 are ...
The significand's leading decimal digit forms from the (0)cde or 100e bits as binary integer. To obtain the trailing significand decimal digits the declet fields 'tttttttttt' have to be decoded according to the DPD rules (see below). The full decimal significand is then obtained by concatenating the leading and trailing decimal digits.
In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. [ 1 ] [ 2 ] It is also known as the shift-and-add -3 algorithm , and can be implemented using a small number of gates in computer hardware, but at the expense of high latency .
In the decimal encoding, it is encoded as a series of p decimal digits (using the densely packed decimal (DPD) encoding). This makes conversion to decimal form efficient, but requires a specialized decimal ALU to process. In the binary integer decimal (BID) encoding, it is encoded as a binary number.
The leading digit is between 0 and 9 (3 or 4 binary bits), and the rest of the significand uses the densely packed decimal (DPD) encoding. The encoding varies depending on whether the most significant 4 bits of the significand are in the range 0 to 7 (0000 2 to 0111 2 ), or higher (1000 2 or 1001 2 ).
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