{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T05:06:53Z","timestamp":1698037613929},"reference-count":4,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":6714,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp; Computers in Japan"],"published-print":{"date-parts":[[1988,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In redundant binary representation, 1, 0 and 1 are used in each digit. It is known that the representation can realize a parallel high\u2010speed addition where a carry propagation over two or more digits is not produced, which helps to execute various functional computations at a high speed. By further extending the idea of the redundant binary representation, the redundant <jats:italic>P<\/jats:italic>\u2010ary representation can be constructed with <jats:italic>P<\/jats:italic> (= 2, 3, 4, \u2026) as the base. In the representation, <jats:italic>K<\/jats:italic> negative integers 0, 1, 2, \u2026, <jats:italic>P<\/jats:italic> \u2010 1, can be used as the digit, in addition to the usual <jats:italic>P<\/jats:italic> positive integers 1, 2, 3, \u2026, <jats:italic>K<\/jats:italic> (= \u2010<jats:italic>K<\/jats:italic>). When <jats:italic>K<\/jats:italic> = 1, the redundant <jats:italic>P<\/jats:italic>\u2010ary representation is called the minimum redundant <jats:italic>P<\/jats:italic>\u2010ary representation. This paper considers the minimum redundant <jats:italic>P<\/jats:italic>\u2010ary representation, and shows that an addition algorithm exists where the carry propagation over more than two digits is not produced for arbitrary base <jats:italic>P<\/jats:italic>, as in the case of the redundant binary representation. By increasing <jats:italic>P<\/jats:italic> in the proposed algorithm, the digits of the data can be reduced which will lead to a high\u2010speed functional computation device with a simple structure.<\/jats:p>","DOI":"10.1002\/scj.4690191104","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T14:48:58Z","timestamp":1183819738000},"page":"33-39","source":"Crossref","is-referenced-by-count":1,"title":["High\u2010speed addition and subtraction using a minimum redundant p\u2010ary representation"],"prefix":"10.1002","volume":"19","author":[{"given":"Takeomi","family":"Tamesada","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TEC.1961.5219227"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1970.223022"},{"key":"e_1_2_1_4_2","first-page":"783","article-title":"VLSI\u2010oriented high\u2010speed multiplier based on redundant binary addition tree","volume":"66","author":"Takagi","year":"1983","journal-title":"Trans. (D) I.E.C.E., Japan"},{"issue":"4","key":"e_1_2_1_5_2","first-page":"450","article-title":"VLSI\u2010oriented high\u2010speed divider based on redundant binary representation","volume":"67","author":"Takagi","year":"1984","journal-title":"Trans. (D) I.E.C.E., Japan"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690191104","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690191104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T03:37:26Z","timestamp":1697945846000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690191104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,11]]},"references-count":4,"journal-issue":{"issue":"11","published-print":{"date-parts":[[1988,11]]}},"alternative-id":["10.1002\/scj.4690191104"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690191104","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,11]]}}}