Fast and Efficient Circuit Topologies forFinding the Maximum of n k-Bit Numbers

Finding the value and/or index of the maximum (or minimum) element of a set of
$n$
numbers (each with
$k$
-bits) is a fundamental arithmetic operation and is needed in many applications. This paper proposes several maximum-finder (or minimum-finder) circuit topologies, which are parallel. We wrote circuit generators at hardware description language level for our topologies and previous works. Then we synthesized these circuits for 20 different
$(n, k)$
cases (with values up to 64) and compared their efficiency in timing (latency), area, and energy. The timing complexity of our fastest topology is O(log
$n$
+ log
$k$
), whereas the fastest in the literature is O(log
$n$
log
$k$
). The synthesis results showed that our fastest topology is 1.2-2.2 times (1.6 times on the average) faster than the state-of-the-art. In this paper, we argue that a more fair metric of area efficiency is area-timing product. In terms of ATP, our proposed topologies are better than the state-of-the-art in 19 out of the 20 cases. In terms of energy (i.e., power-timing product, abbreviated as PTP), we are better in 11 cases out of 20.