Application of Boolean algebra to switching circuit design and to error detection

@article{Muller1954ApplicationOB,
  title={Application of Boolean algebra to switching circuit design and to error detection},
  author={David E. Muller},
  journal={Trans. I R E Prof. Group Electron. Comput.},
  year={1954},
  volume={3},
  pages={6-12}
}
  • D. E. Muller
  • Published 1 September 1954
  • Computer Science
  • Trans. I R E Prof. Group Electron. Comput.
A solution is sought to the general problem of simplifying switching circuits that have more than one output. The mathematical treatment of the problem applies only to circuits that may be represented by “polynomials” in Boolean algebra. It is shown that certain parts of the multiple output problem for such circuits may be reduced to a single output problem whose inputs are equal in number to the sum of the numbers of inputs and outputs in the original problem. A particularly simple reduction… 

Automatic fault detection in combinational switching networks

This paper describes an IBM 7090 program for the design of single output combinational switching circuits for arbitrary sets of primitive logical elements, designed so that the most promising sequences are investigated first.

Applications of Multi-Terminal Binary Decision Diagrams

An efficient algorithm is given for handling arithmetic operations and relations in the verification of an SRT division algorithm similar to the one that is used in the Pentium and it is proved that the time complexity of the algorithm is linear in the number of variables.

A study of arithmetic circuits and the effect of utilising Reed-Muller techniques.

This project investigates existing Reed-Muller algebraic techniques and explores their application in arithmetic circuits and shows that, although Boolean logic is believed to be a more general tool in logic design, it is not the best tool in all situations.

Complexity Lower Bound for Boolean Functions in the Class of Extended Operator Forms

  • A. S. Baliuk
  • Computer Science, Mathematics
    The Bulletin of Irkutsk State University. Series Mathematics
  • 2019
A lower bound for the complexity of Boolean functions in the class of extended operator forms is obtained using an algebraic extension of a finite field of order 2, which strengthens the previously known lower bounds for this class.

Multilevel logic synthesis for arithmetic functions

This paper presents a process of redundancy removal which reduces many XOR gates to single AND or OR gates without altering the functional behavior of the network and produces circuits, before and after technology mapping.

Algorithms in computer-aided design of VLSI circuits

Two algorithms based on Genetic Algorithm and GA with Simulated Annealing are presented for the placement of symmetrical FPGA and could achieve comparable results to those obtained by Versatile Placement and Routing tools in terms of the number of routing channel tracks.

Unateness Properties of and-Exclusive-or Logic Circuits

An algorithm is presented which allows simple determination of a ring sum realization using logic array notation, and which can be used to find minimum cost polarities and a second algorithm which allows nonexhaustive and near-optimal handling of functions with DON'T CARE conditions.

Cyclic Boolean circuits

Combinational logic synthesis based on the dual form of Reed-Muller representation

To search for the optimal polarity for large number of variables and to reduce the se arch time 0 ffinding the 0 ptimal polarity 0 fthe function, two new algorithms are developed and presented in this thesis.

Hybrid decision diagrams

An efficient algorithm to implement arithmetic operations efficiently for hybrid decision diagrams for functions that map boolean vectors into the integers and it is proved that for the class of linear expressions, the time complexity of the algorithm is linear in the number of variables.
...