We determine what information about failures is necessary and sufficient to solve Consensus in asynchronous distributed systems subject to crash failures. In [CT91], we proved that W, a failure detector that provides surprisingly little information about which processes have crashed, is sufficient to solve Consensus in asynchronous systems with a majority of correct processes. In this paper, we prove that to solve Consensus, any failure detector has to provide at least as much information as W. Thus, W is indeed the weakest failure detector for solving Consensus in asynchronous systems with a majority of correct processes.