Volume 15, 2003

University of Bialystok

Copyright (c) 2003 Association of Mizar Users

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

- 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.

- Preliminaries
- Majorant Power
- 2's Complement

- [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.

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