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

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