Binary and quaternary sequences are the most important sequences in view of many practical applications. Any quaternary sequence
can be decomposed into two binary sequences and any two binary sequences can be combined into a quaternary sequence using
the Gray mapping. We analyze the relation between the measures of pseudorandomness for the two binary sequences and the measures
for the corresponding quaternary sequences, which were both introduced by Mauduit and Sárközy. Our results show that each
‘pseudorandom’ quaternary sequence corresponds to two ‘pseudorandom’ binary sequences which are ‘uncorrelated’.