IEICE TRANSACTIONS on Electronics
Systematic Interpretation of Redundant Arithmetic Adders in Binary and Multiple-Valued Logic
Summary :
This paper presents an algorithm-level interpretation of fast adder structures in binary/multiple-valued logic. The key idea is to employ a unified representation of addition algorithms called Counter Tree Diagrams (CTDs). The use of CTDs makes it possible to describe and analyze addition algorithms at various levels of abstraction. A high-level CTD represents a network of coarse-grained components associated with multiple-valued logic devices, while a low-level CTD represents a network of primitive components directly mapped onto binary logic devices. The level of abstraction in circuit representation can be changed by decomposition of CTDs. We can derive possible variations of adder structures by decomposing a high-level CTD into low-level CTDs. This paper demonstrates the interpretation of redundant arithmetic adders based on CTDs. We first introduce an extension of CTDs to represent possible redundant arithmetic adders with limited carry propagation. Using the extended version of CTDs, we can classify the conventional adder structures including those using emerging devices into three types in a systematic way.
- Publication
- IEICE TRANSACTIONS on Electronics Vol.E89-C No.11 pp.1645-1654
- Publication Date
- 2006/11/01
- Publicized
- Online ISSN
- 1745-1353
- DOI
- 10.1093/ietele/e89-c.11.1645
- Type of Manuscript
- Special Section PAPER (Special Section on Novel Device Architectures and System Integration Technologies)
- Category
Authors
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Naofumi HOMMA, Takafumi AOKI, Tatsuo HIGUCHI, "Systematic Interpretation of Redundant Arithmetic Adders in Binary and Multiple-Valued Logic" in IEICE TRANSACTIONS on Electronics,
vol. E89-C, no. 11, pp. 1645-1654, November 2006, doi: 10.1093/ietele/e89-c.11.1645.
Abstract: This paper presents an algorithm-level interpretation of fast adder structures in binary/multiple-valued logic. The key idea is to employ a unified representation of addition algorithms called Counter Tree Diagrams (CTDs). The use of CTDs makes it possible to describe and analyze addition algorithms at various levels of abstraction. A high-level CTD represents a network of coarse-grained components associated with multiple-valued logic devices, while a low-level CTD represents a network of primitive components directly mapped onto binary logic devices. The level of abstraction in circuit representation can be changed by decomposition of CTDs. We can derive possible variations of adder structures by decomposing a high-level CTD into low-level CTDs. This paper demonstrates the interpretation of redundant arithmetic adders based on CTDs. We first introduce an extension of CTDs to represent possible redundant arithmetic adders with limited carry propagation. Using the extended version of CTDs, we can classify the conventional adder structures including those using emerging devices into three types in a systematic way.
URL: https://global.ieice.org/en_transactions/electronics/10.1093/ietele/e89-c.11.1645/_p
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@ARTICLE{e89-c_11_1645,
author={Naofumi HOMMA, Takafumi AOKI, Tatsuo HIGUCHI, },
journal={IEICE TRANSACTIONS on Electronics},
title={Systematic Interpretation of Redundant Arithmetic Adders in Binary and Multiple-Valued Logic},
year={2006},
volume={E89-C},
number={11},
pages={1645-1654},
abstract={This paper presents an algorithm-level interpretation of fast adder structures in binary/multiple-valued logic. The key idea is to employ a unified representation of addition algorithms called Counter Tree Diagrams (CTDs). The use of CTDs makes it possible to describe and analyze addition algorithms at various levels of abstraction. A high-level CTD represents a network of coarse-grained components associated with multiple-valued logic devices, while a low-level CTD represents a network of primitive components directly mapped onto binary logic devices. The level of abstraction in circuit representation can be changed by decomposition of CTDs. We can derive possible variations of adder structures by decomposing a high-level CTD into low-level CTDs. This paper demonstrates the interpretation of redundant arithmetic adders based on CTDs. We first introduce an extension of CTDs to represent possible redundant arithmetic adders with limited carry propagation. Using the extended version of CTDs, we can classify the conventional adder structures including those using emerging devices into three types in a systematic way.},
keywords={},
doi={10.1093/ietele/e89-c.11.1645},
ISSN={1745-1353},
month={November},}
Copy
TY - JOUR
TI - Systematic Interpretation of Redundant Arithmetic Adders in Binary and Multiple-Valued Logic
T2 - IEICE TRANSACTIONS on Electronics
SP - 1645
EP - 1654
AU - Naofumi HOMMA
AU - Takafumi AOKI
AU - Tatsuo HIGUCHI
PY - 2006
DO - 10.1093/ietele/e89-c.11.1645
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E89-C
IS - 11
JA - IEICE TRANSACTIONS on Electronics
Y1 - November 2006
AB - This paper presents an algorithm-level interpretation of fast adder structures in binary/multiple-valued logic. The key idea is to employ a unified representation of addition algorithms called Counter Tree Diagrams (CTDs). The use of CTDs makes it possible to describe and analyze addition algorithms at various levels of abstraction. A high-level CTD represents a network of coarse-grained components associated with multiple-valued logic devices, while a low-level CTD represents a network of primitive components directly mapped onto binary logic devices. The level of abstraction in circuit representation can be changed by decomposition of CTDs. We can derive possible variations of adder structures by decomposing a high-level CTD into low-level CTDs. This paper demonstrates the interpretation of redundant arithmetic adders based on CTDs. We first introduce an extension of CTDs to represent possible redundant arithmetic adders with limited carry propagation. Using the extended version of CTDs, we can classify the conventional adder structures including those using emerging devices into three types in a systematic way.
ER -
English
