Stability of n -Bit Generalized Full Adder Circuits (GFAs). Part II
Katsumi Wasaki
Formalized Mathematics, Tome 16 (2008), p. 73-80 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We continue to formalize the concept of the Generalized Full Addition and Subtraction circuits (GFAs), define the structures of calculation units for the Redundant Signed Digit (RSD) operations, then prove its stability of the calculations. Generally, one-bit binary full adder assumes positive weights to all of its three binary inputs and two outputs. We define the circuit structure of two-types n-bit GFAs using the recursive construction to use the RSD arithmetic logical units that we generalize full adder to have both positive and negative weights to inputs and outputs. The motivation for this research is to establish a technique based on formalized mathematics and its applications for calculation circuits with high reliability.MML identifier: GFACIRC2, version: 7.8.09 4.97.1001

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:266606 
@article{bwmeta1.element.doi-10_2478_v10037-008-0011-5,
     author = {Katsumi Wasaki},
     title = {
      Stability of
      n
      -Bit Generalized Full Adder Circuits (GFAs). Part II
    },
     journal = {Formalized Mathematics},
     volume = {16},
     year = {2008},
     pages = {73-80},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0011-5}
}

Katsumi Wasaki. 
      Stability of
      n
      -Bit Generalized Full Adder Circuits (GFAs). Part II
    . Formalized Mathematics, Tome 16 (2008) pp. 73-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0011-5/

[1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858

[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[4] Grzegorz Bancerek and Yatsuka Nakamura. Full adder circuit. Part I. Formalized Mathematics, 5(3):367-380, 1996.

[5] Grzegorz Bancerek, Shin'nosuke Yamaguchi, and Katsumi Wasaki. Full adder circuit. Part II. Formalized Mathematics, 10(1):65-71, 2002.

[6] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

[7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[8] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[9] Yatsuka Nakamura and Grzegorz Bancerek. Combining of circuits. Formalized Mathematics, 5(2):283-295, 1996.

[10] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Introduction to circuits, I. Formalized Mathematics, 5(2):227-232, 1996.

[11] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, II. Formalized Mathematics, 5(2):215-220, 1996.

[12] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.

[13] Andrzej Trybulec. Many-sorted sets. Formalized Mathematics, 4(1):15-22, 1993.

[14] Andrzej Trybulec. Many sorted algebras. Formalized Mathematics, 5(1):37-42, 1996.

[15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[16] Edmund Woronowicz. Many-argument relations. Formalized Mathematics, 1(4):733-737, 1990.

[17] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

[18] Shin'nosuke Yamaguchi, Katsumi Wasaki, and Nobuhiro Shimoi. Generalized full adder circuits (GFAs). Part I. Formalized Mathematics, 13(4):549-571, 2005.