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| | In [[computing]] canonical-signed-digit (CSD) is a [[number system]] for encoding a [[floating-point]] value in a [[two's complement]] representation. This encoding contains 33% fewer non-zeros than the two's complement form, leading to efficient implementations of add/subtract networks in hardwired [[Digital signal processing]]. |
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| | The representation uses a sequence of one or more of the symbols, -1, 0, +1 (alternatively -, 0 or +) with each position possibly representing the addition or subtraction of a power of 2. For instance 23 is represented as +0-00-, which expands to <math>+2^5 -2^3 -2^0</math> or <math>32 - 8 - 1 = 23</math> |
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| | ==Implementation== |
| | CSD is obtained by transforming every sequence of zero followed by ones (011...1) into + followed by zeros and the least significant bit by - (+0....0-). |
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| | As an example: the number 7 has a two's complement representation 0111 |
| | :<math>(7=0\times 2^3+1\times 2^2+1\times 2^1+1\times 2^0 = 4+2+1)</math> |
| | into +00- |
| | :<math>(7=+1\times 2^3+0\times 2^2+0\times 2^1-1\times 2^0 = 8-1)</math> |
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| | ==External links== |
| | * {{cite web | title = Fractions in the Canonical-Signed-Digit Number System | id = {{citeseerx|10.1.1.126.5477}} }} |
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| | [[Category:Computing terminology]] |
Revision as of 22:19, 9 December 2013
In computing canonical-signed-digit (CSD) is a number system for encoding a floating-point value in a two's complement representation. This encoding contains 33% fewer non-zeros than the two's complement form, leading to efficient implementations of add/subtract networks in hardwired Digital signal processing.
The representation uses a sequence of one or more of the symbols, -1, 0, +1 (alternatively -, 0 or +) with each position possibly representing the addition or subtraction of a power of 2. For instance 23 is represented as +0-00-, which expands to or
Implementation
CSD is obtained by transforming every sequence of zero followed by ones (011...1) into + followed by zeros and the least significant bit by - (+0....0-).
As an example: the number 7 has a two's complement representation 0111
into +00-
External links