Deafness has been associated with poor abilities to deal with digits in the context of arithmetic and memory, and language modality-specific differences in the phonological similarity of digits have been shown to influence short-term memory (STM). Therefore, the overall aim of the present thesis was to find out whether language modality-specific differences in phonological processing between sign and speech can explain why deaf signers perform at lower levels than hearing peers when dealing with digits. To explore this aim, the role of phonological processing in digit-based arithmetic and memory tasks was investigated, using both behavioural and neuroimaging methods, in adult deaf signers and hearing non-signers, carefully matched on age, sex, education and nonverbal intelligence. To make task demands as equal as possible for both groups, and to control for material effects, arithmetic, phonological processing, STM and working memory (WM) were all assessed using the same presentation and response mode for both groups. The results suggested that in digit-based STM, phonological similarity of manual numerals causes deaf signers to perform more poorly than hearing non-signers. However, for digit-based WM there was no difference between the groups, possibly due to differences in allocation of resources during WM. This indicates that similar WM for the two groups can be generalized from lexical items to digits. Further, we found that in the present work deaf signers performed better than expected and on a par with hearing peers on all arithmetic tasks, except for multiplication, possibly because the groups studied here were very carefully matched. However, the neural networks recruited for arithmetic and phonology differed between groups. During multiplication tasks, deaf signers showed an increased reliance on cortex of the right parietal lobe complemented by the left inferior frontal gyrus. In contrast, hearing non-signers relied on cortex of the left frontal and parietal lobe during multiplication. This suggests that while hearing non-signers recruit phonology-dependent arithmetic fact retrieval processes for multiplication, deaf signers recruit non-verbal magnitude manipulation processes. For phonology, the hearing non-signers engaged left lateralized frontal and parietal areas within the classical perisylvian language network. In deaf signers, however, phonological processing was limited to cortex of the left occipital lobe, suggesting that sign-based phonological processing does not necessarily activate the classical language network. In conclusion, the findings of the present thesis suggest that language modality-specific differences between sign and speech in different ways can explain why deaf signers perform at lower levels than hearing non-signers on tasks that include dealing with digits.