Η άθροιση μεγάλων αριθμών είναι μια χρονοβόρα και ενεργοβόρα διαδικασία. Πολλές μέθοδοι έχουν αναπτυχθεί για να μειωθεί η καθυστέρηση υπολογισμού του αθροίσματος λόγω της μετάδοσης κρατουμένου. Τέτοιες είναι η πρόβλεψη κρατουμένου (carry look ahead) και η επιλογή κρατουμένου (carry select). Αυτές οι αρχιτεκτονικές δεν είναι επαρκώς επεκτάσιμες για μεγάλους αριθμούς (με πολλά bits) ή πολλούς αριθμούς, διότι παράγονται μεγάλα και ενεργοβόρα κυκλώματα. Στην παρούσα εργασία μελετάται η μέθοδος υπολοίπου (RNS), η οποία χρησιμοποιεί συστήματα αριθμών μεγαλύτερα από το δυαδικό. Ορίζεται μια βάση τριών αριθμών και οι αριθμοί αναπαρίστανται στα εκάστοτε τρία συστήματα της βάσης. Η άθροιση γίνεται παράλληλα σε κάθε σύστημα και τέλος οι αριθμοί μετατρέπονται πάλι στο δυαδικό. Τα πλεονεκτήματα αυτής της προσέγγισης είναι η παραλληλία και η απουσία μεγάλων κυκλωμάτων διάδοσης κρατουμένου. Το μειονέκτημα είναι ότι χρειάζονται κυκλώματα μετατροπής από και προς το δυαδικό σύστημα. Αυτού του είδους οι αθροιστές συγκρίνονται για κατανάλωση ενέργειας με τους γνωστούς carry look ahead και carry select. Διαπιστώθηκε ότι οι RNS αθροιστές καταναλώνουν λιγότερη ενέργεια. / The addition of many-bits numbers is a time and power consuming task. Many methods are developed to reduce the sum calculation delay due to carry propagation. Such techniques are Carry Look Ahead and Carry Select, Those techniques are not scalable to many bits numbers or a set of many numbers: the circuits needed are big and power consuming. In this thesis, the the RNS technique is investigated. This technique uses radix bigger than binary. A 3-numbers base is defined and the numbers that participate in the sum are represented uniquely in each element radix. The addition is performed in parallel in each radix. Finally the result is transformed back to the binary numbers system. The advantages of this technique are the parallelization of the process and the lack of carry propagation circuits. The disadvantage is that transformation circuits are need from/to binary system. The RNS adders are compared to CLA and CS for power. Such adders are compared to CLA and CS for power consumption. It is found that RNS adders consume less energy.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work stems from a project developed under the Teaching and Learning of Mathematics and their Philosophical, Historical and Epistemological Foundations research scope of the Graduate Program in Mathematics Education and Physics Teaching at the Federal University of Santa Maria. Based on the assumptions of the Historic-Cultural Theory and the Theory of Activity, as well as authors who address the training of teachers who teach mathematics, we define as main objective to investigate the formation of teachers who teach Mathematics in the early years of Elementary school, from discussions about the Decimal Numbering System in the context of a working group of Guiding Studies of Pacto Nacional pela Alfabetização na Idade Certa (PNAIC) Program. How collected data procedure, we adopted a questionnaire applied to Guiding Studies of this Program belonging to Santa Maria (RS) polo; follow-up of continuing education presential meetings that boarded the Decimal Numbering System in one of the working groups and we realize reflective sessions with guiding studies teachers of this working group. While the questionnaire answers served to bring indicative of these teachers think about Decimal Numbering Decimal and your teaching, the data of continuing education meetings and reflective sessions were systematized in four analysis sections the teacher as subject in your formation; the math knowledge as promotor of subject development; pedagogical intentionality as element of teacher organization, e; the share as promotor of comprehension of complexity of pedagogical activity with the goal of build episodes (Moura,1992) to verify the extent to which the Guiding Studies presents quality change in your formation process. We conclude that formation space, such as offered by PNAIC, may constitute as Learning spaces of Teaching for evolved teachers, since that develop forming activities that provide access to math knowledge as a result of logic-historic process; provide discussions about Teaching organization focusing in Learning of student and favor the collective development of group, in order that knowledge appropriation occurs from the social to the individual. / Este trabalho decorre de um projeto desenvolvido no âmbito da linha de pesquisa Ensino e Aprendizagem da Matemática e seus Fundamentos Filosóficos, Históricos e Epistemológicos do Programa de Pós-Graduação em Educação Matemática e Ensino de Física da Universidade Federal de Santa Maria. Com base nos pressupostos da Teoria Histórcio-Cultural e da teoria da Atividade, assim como em autores que abordam a formação de professores que ensinam Matemática, delimita-se como objetivo principal investigar a formação de professores que ensinam Matemática nos anos iniciais do Ensino Fundamental, a partir de discussões sobre o Sistema de Numeração Decimal, no contexto de um grupo de trabalho de Orientadoras de Estudos do programa Pacto Nacional pela Alfabetização na Idade Certa (PNAIC). Como procedimento de coletada de dados foram adotados um questionário aplicado a Orientadores de Estudos desse programa, pertencentes ao polo de Santa Maria (RS); o acompanhamento dos encontros de formação continuada presenciais que abordaram o Sistema de Numeração Decimal em um dos grupos de trabalho e a realização de sessões reflexivas com professores Orientadores de Estudos desse grupo de trabalho. As respostas dos questionários serviram para levantar indicativos do que estes professores pensam sobre o Sistema de Numeração Decimal e o seu ensino. Os dados dos encontros de formação e das sessões reflexivas foram sistematizados em quadro unidades de análise - o professor como sujeito de sua formação; o conhecimento matemático como promotor de desenvolvimento do sujeito; a intencionalidade pedagógica como elemento da organização do ensino; e o compartilhamento como promotor da compreensão da complexidade da atividade pedagógica com o intuito de constituir episódios (Moura, 1992) para verificar em que medida os Orientadores de Estudos apresentaram mudanças de qualidade nos seu processo de formação. Concluímos que espaços de formação, como os oportunizados pelo PNAIC, podem se constituir como espaços de aprendizagem da docência para os professores envolvidos, em especial, se desenvolverem atividades formadoras que proporcionem o acesso ao conhecimento matemático como decorrência de um processo lógico-histórico; promoverem discussões sobre a organização do ensino com enfoque no aprendizado do aluno e favorecerem o desenvolvimento coletivo do grupo, a partir da compreensão do papel fundamental das relações sociais no desenvolvimento do indivíduo.