Two operand binary adders with Threshold Logic
The central topic of this paper is the implementation of binary adders with Threshold Logic using a new methodology that introduces two innovations: the use of the input and output carries of each bit for obtaining all the sum bits and a modification of the classic Carry Lookahead adder technique that allows us to obtain the expressions of the generation and propagation carries in a more appropriate way for Threshold Logic. In this way, it has been possible to systematize the process of design of a binary adder with Threshold Logic relating all its important parameters: number of bits of the operands, depth, size, maximum fan-in, and maximum weight. The results obtained are an improvement on those published to date and are summarized as follows: Depth 2 adder: s = 2n, omega(max) = 2(n), f(max) = 2n + 1. Depth 3 adder: s = 4n - 2[n/\root n\], omega(max) = 2([n/\root n\]), f(max) = 2[n/\root n\] + 1. Depth d adder (asymptotic behavior): s = O(n), omega(max) = O(2(root n)), f(max) = O((e-1)root n). If the weights are bounded by omega(max):n(max) = O(log(d-1) u(max)), d(min) = O(log n/log(log omega(max))).
binary adders threshold logic computer arithmetic logic design threshold gate neural networks