Volume 14, 2002

University of Bialystok

Copyright (c) 2002 Association of Mizar Users

**Grzegorz Bancerek**- Bialystok Technical University
**Shin'nosuke Yamaguchi**- Shinshu University, Nagano
**Katsumi Wasaki**- Shinshu University, Nagano

- In this article we continue the investigations from [5] of verification of a design of adder circuit. We define it as a combination of 1-bit adders using schemes from [6]. $n$-bit adder circuit has the following structure\\ \input FACIRC_2.PIC As the main result we prove the stability of the circuit. Further works will consist of the proof of full correctness of the circuit.

Contents (PDF format)

- [1]
Grzegorz Bancerek.
Cardinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Grzegorz Bancerek.
Curried and uncurried functions.
*Journal of Formalized Mathematics*, 2, 1990. - [4]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Grzegorz Bancerek and Yatsuka Nakamura.
Full adder circuit. Part I.
*Journal of Formalized Mathematics*, 7, 1995. - [6]
Grzegorz Bancerek, Shin'nosuke Yamaguchi, and Yasunari Shidama.
Combining of multi cell circuits.
*Journal of Formalized Mathematics*, 14, 2002. - [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.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [11]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Yatsuka Nakamura and Grzegorz Bancerek.
Combining of circuits.
*Journal of Formalized Mathematics*, 7, 1995. - [13]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Preliminaries to circuits, II.
*Journal of Formalized Mathematics*, 6, 1994. - [14]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Introduction to circuits, II.
*Journal of Formalized Mathematics*, 7, 1995. - [15]
Takaya Nishiyama and Yasuho Mizuhara.
Binary arithmetics.
*Journal of Formalized Mathematics*, 5, 1993. - [16]
Andrzej Trybulec.
Enumerated sets.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [18]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [19]
Andrzej Trybulec.
Many-sorted sets.
*Journal of Formalized Mathematics*, 5, 1993. - [20]
Andrzej Trybulec.
Many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [21]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [22]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [23]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [24]
Edmund Woronowicz.
Many-argument relations.
*Journal of Formalized Mathematics*, 2, 1990.

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