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.
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]
-
Preliminaries
-
Majorant Power
-
2's Complement
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Received January 30, 2003
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