### 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) |
---|---|

Pages (from-to) | 391-399 |

Number of pages | 9 |

Journal | IEEE Transactions on Computers |

Volume | C-17 |

Issue number | 4 |

DOIs | |

State | Published - 1968 |

Externally published | Yes |

### Fingerprint

### 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

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

### Cite this

*IEEE Transactions on Computers*,

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

**Realization of a Class of Switching Functions by Threshold-Logic Networks.** / Yau, Sik-Sang; Ostapko, D. L.

Research output: Contribution to journal › Article

*IEEE Transactions on Computers*, vol. C-17, no. 4, pp. 391-399. https://doi.org/10.1109/TC.1968.229390

}

TY - JOUR

T1 - Realization of a Class of Switching Functions by Threshold-Logic Networks

AU - Yau, Sik-Sang

AU - Ostapko, D. L.

PY - 1968

Y1 - 1968

N2 - 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.

AB - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=44349087102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44349087102&partnerID=8YFLogxK

U2 - 10.1109/TC.1968.229390

DO - 10.1109/TC.1968.229390

M3 - Article

AN - SCOPUS:44349087102

VL - C-17

SP - 391

EP - 399

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 4

ER -