### Abstract

Inthis note, a class of switching functions, called threshold-product functions, whose definition is analogous to that of threshold functions (which will be called threshold-sum functions), is studied in detail. It is shown that both threshold functions and parity functions are special cases of threshold-product functions. A simple and economical threshold-logic realization method is established for threshold-product functions. This economical realization method is based on constrained solutions for threshold-product functions. A systematic technique for finding a constrained solution for a threshold-product function is obtained, and this technique can be employed for testing whether a switching function is a threshold-product function as well. When the number of variables in a switching function is not large, say no more than 6, a simpler method for the above purposes is found. Furthermore, a threshold-logic realization method which yields a minimal realization for certain threshold-product functions is obtained.

Original language | English (US) |
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Pages (from-to) | 391-399 |

Number of pages | 9 |

Journal | IEEE Transactions on Computers |

Volume | C-17 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1968 |

Externally published | Yes |

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### Keywords

- Economical and minimal threshold-logic realizations constrained solutions techniques and properties parity functions switching functions threshold-logic networks threshold-product functions threshold-sum functions

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Computers*,

*C-17*(4), 391-399. https://doi.org/10.1109/TC.1968.229390