Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

A Representation of Integers by Binary Arithmetics and Addition of Integers


Hisayoshi Kunimune
Shinshu University, Nagano
Yatsuka Nakamura
Shinshu University, Nagano

Summary.

In this article, we introduce the new concept of 2's complement representation. Natural numbers that are congruent mod $n$ can be represented by the same $n$ bits binary. Using the concept introduced here, negative numbers that are congruent mod $n$ also can be represented by the same $n$ bit binary. We also show some properties of addition of integers using this concept.

MML Identifier: BINARI_4

The terminology and notation used in this paper have been introduced in the following articles [16] [21] [2] [5] [12] [11] [10] [9] [17] [13] [15] [6] [7] [1] [14] [18] [3] [20] [8] [4] [19]

Contents (PDF format)

  1. Preliminaries
  2. Majorant Power
  3. 2's Complement

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[6] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[7] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[8] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[9] Robert Milewski. Binary arithmetics. Binary sequences. Journal of Formalized Mathematics, 10, 1998.
[10] Yasuho Mizuhara and Takaya Nishiyama. Binary arithmetics, addition and subtraction of integers. Journal of Formalized Mathematics, 6, 1994.
[11] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
[12] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms. Journal of Formalized Mathematics, 2, 1990.
[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] Michal J. Trybulec. Integers. Journal of Formalized Mathematics, 2, 1990.
[17] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[18] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[20] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[21] Edmund Woronowicz. Many-argument relations. Journal of Formalized Mathematics, 2, 1990.

Received January 30, 2003


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