Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

Binary Arithmetics


Takaya Nishiyama
Shinshu University, Information Engineering Dept., Nagano
Yasuho Mizuhara
Shinshu University, Information Engineering Dept., Nagano

Summary.

Formalizes the basic concepts of binary arithmetic and its related operations. We present the definitions for the following logical operators: 'or' and 'xor' (exclusive or) and include in this article some theorems concerning these operators. We also introduce the concept of an $n$-bit register. Such registers are used in the definition of binary unsigned arithmetic presented in this article. Theorems on the relationships of such concepts to the operations of natural numbers are also given.

MML Identifier: BINARITH

The terminology and notation used in this paper have been introduced in the following articles [14] [9] [17] [2] [3] [15] [1] [19] [18] [7] [8] [6] [4] [13] [12] [10] [5] [11] [16]

Contents (PDF format)

Acknowledgments

Many thanks to Professor Andrzej Trybulec for making this article a success. We really enjoyed working with you...ARIGATOU GOZAIMASHITA.

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. Sequences of ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek. Monoids. Journal of Formalized Mathematics, 4, 1992.
[5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[11] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[12] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[13] Konrad Raczkowski and Andrzej Nedzusiak. Series. Journal of Formalized Mathematics, 3, 1991.
[14] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[15] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[16] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[17] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[18] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[19] Edmund Woronowicz. Many-argument relations. Journal of Formalized Mathematics, 2, 1990.

Received October 8, 1993

[ Download a postscript version, MML identifier index, Mizar home page]