Acquisition delays have been found for scope assignments and scalar implicatures (cf. Musolino 1998; Lidz 2016; Chierchia et al. 2001; Noveck 2001; Katsos & Bishop 2011). Both acquisition delays have separately been attributed to childrenís immature processing capacities, like their limited working memory. Yet, no study has ever directly looked at the role of processing limits in the acquisition of scope assignments or in the acquisition of scalar implicatures. Moreover, no one has looked at the two fields in combination. Therefore, this paper aims to investigate English-speaking childrenís mastery of scope assignments as well as their command of scalar implicatures. Most importantly, I also tested each childís digit span which is generally used to measure working memory. The results showed that although inverse-scope readings are allowed in English, adults hesitated to accept them but children were more permissive. Moreover, a significant correlation was found between participantsí acceptance of inverse-scope readings and their digit span. Regarding scalar implicatures, children did not compute the scalar implicatures while adults did, and a significant correlation was observed between a childís computation of scalar implicatures and their digit span. These findings provide new support for the processing approaches to the observed delays in scope assignments and scalar implicatures.