In this paper the effects of quantisation on distributed convex optimisation algorithms are explored via the lens of monotone operator theory. Specifically, by representing transmission quantisation via an additive noise model, we demonstrate how quantisation can be viewed as an instance of an inexact Krasnosel' skiľ-Mann scheme. In the case of two distributed solvers, the Alternating Direction Method of Multipliers and the Primal Dual Method of Multipliers, we further demonstrate how an adaptive quantisation scheme can be constructed to reduce transmission costs between nodes. Finally for the Gaussian channel capacity maximisation problem, we demonstrate convergence even in the presence of one-bit uniform quantisation based on the aforementioned adaptive quantisation scheme.