Parallel Binary Adders with a Minimum Number of Connections

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.