Thesis (Ph. D.)--Lehigh University, 2004. / Includes vita. Includes bibliographical references (leaves 205-221).

Abstract of Thesis (Ph. D.)--Ohio state University, 1925.

Thesis (Ph. D.)--Catholic University of America, 1926. / Published also as Catholic University of America. Educational research bulletins ... vol. I, nos. 4-5. Bibliography: p. 71-74.

Thesis (Ph. D.)--Lehigh University, 2003. / Includes vita. Includes bibliographical references (leaves 125-136).

This dissertation focuses on improving the non-restoring division and square root algorithm. Although the non-restoring division algorithm is the fastest and has less complexity among other radix-2 digit recurrence division algorithms, there are some possibilities to enhance its performance. To improve its performance, two new approaches are proposed here. In addition, the research scope is extended to seek an efficient algorithm for implementing non-restoring square root, which has similar steps to non-restoring division. For the first proposed approach, the non-restoring divider with a modified algorithm is presented. The new algorithm changes the order of the flowchart, which reduces one unit delay of the multiplexer per every iteration. In addition, a new method to find a correct quotient is presented and it removes an error that the quotient is always odd number after a digit conversion from a digit converter from the quotient with digits 1 and -1 to conventional binary number. The second proposed approach is a novel method to find a quotient bit for every iteration, which hides the total delay of the multiplexer with dual path calculation. The proposed method uses a Most Significant Carry (MSC) generator, which determines the sign of each remainder faster than the conventional carry lookahead adder and it eventually reduces the total delay by almost 22% compared to the conventional non-restoring division algorithm. Finally, an improved algorithm for non-restoring square root is proposed. The two concepts already applied to non-restoring division are adopted for improving the performance of a non-restoring square root since it has similar process to that of non-restoring division for finding square root. Additionally, a new method to find intermediate quotients is presented that removes an adder per an iteration to reduce the total area and power consumption. The non-restoring square root with MSC generator reduces total delay, area and power consumption significantly. / text

This study investigated domains within the tasks of ordination, cardination and natural number. In addition, it examined the sequencing of the development of established domains between ordination, cardination and natural number. One hundred and forty-eight children were individually given a test designed to ascertain the presence of arithmetic related skills. The task of cardination was designed to detect the ability to associate numbers with sets containing a group of elements ranging from one to five. The task of ordination was designed to detect the ability to associate a number with a relative position within a group of ordered objects. The task of natural number assessed children's ability to add numbers with a sum equal to five or less. Latent structure analysis was used to analyze the results. Four different models were used in order to establish domains within each task. The four models that were used tested independence, equiprobability, ordered relations and asymmetrical equivalence. The results showed two domains for cardination. One item in a set constituted one domain while three and five items in a set constituted a second domain. The domain for ordination included relative positions one, three and five. In regards to natural number, the results showed a permeable domain. There was some indication of ordering but it was not strong enough to yield separate domains. The same models were then used to compare across the different tasks. The results showed that the easiest cardination domain developed before ordination and natural number. The results also showed that the ordination task was equivalent to one of the natural number tasks. All of the other comparisons between cardination, ordination and natural number yielded asymmetrically equivalent relations. That is, there was an ordering but the ordering was not strong enough to establish separate domains.

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