Journal of Formalized Mathematics
Volume 7, 1995
University of Bialystok
Copyright (c) 1995 Association of Mizar Users

Full Adder Circuit. Part I


Grzegorz Bancerek
Institute of Mathematics, Polish Academy of Sciences
Yatsuka Nakamura
Shinshu University, Nagano

Summary.

We continue the formalisation of circuits started by Piotr Rudnicki, Andrzej Trybulec, Pauline Kawamoto, and the second author in [12], [13], [11], [14]. The first step in proving properties of full $n$-bit adder circuit, i.e. 1-bit adder, is presented. We employ the notation of combining circuits introduced in [10].

This work was written while the first author visited Shinshu University, July--August 1994.

MML Identifier: FACIRC_1

The terminology and notation used in this paper have been introduced in the following articles [17] [16] [21] [20] [1] [18] [22] [4] [5] [3] [9] [7] [8] [23] [15] [2] [6] [19] [13] [14] [10]

Contents (PDF format)

  1. Combining of Many Sorted Signatures
  2. Combining of Circuits
  3. Signatures with One Operation
  4. Unsplit Condition
  5. One Gate Circuits
  6. Boolean Circuits
  7. One Bit Adder

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[8] 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.
[9] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[10] Yatsuka Nakamura and Grzegorz Bancerek. Combining of circuits. Journal of Formalized Mathematics, 7, 1995.
[11] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Introduction to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[12] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[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 algebras. Journal of Formalized Mathematics, 6, 1994.
[20] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[23] Edmund Woronowicz. Many-argument relations. Journal of Formalized Mathematics, 2, 1990.

Received August 10, 1995


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