### Abstract

An n-bit parallel binary adder consisting of NOR gates only in single-rail input logic is proved to require at least 17n + 1 connections for any value of n. Such an adder is proved to require at least 7n + 2 gates. An adder that attains these minimal values is shown. Also, it is concluded that some of the parallel adders with the minimum number of NOR gates derived by Lai and Muroga have the minimum number of connections as well as the minimum number of gates, except for the two modules for the two least significant bit positions. In general, it is extremely difficult to prove the minimality of the number of gates in an arbitrarily large logic network, and it is even more difficult to prove the minimality of the number of connections. Both problems have been solved for n-bit adders of NOR gates in single-rail input logic.

Original language | English |
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Pages (from-to) | 969-976 |

Number of pages | 8 |

Journal | IEEE Transactions on Computers |

Volume | C-32 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1983 Oct |

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### Keywords

- Adder with a minimum number of connections
- NOR gates
- logic design
- minimal adder
- parallel adder
- ripple adder

### ASJC Scopus subject areas

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

### Cite this

*IEEE Transactions on Computers*,

*C-32*(10), 969-976. https://doi.org/10.1109/TC.1983.1676144