  We show that the problem of code construction for multiple access channel
(MAC) resolvability can be reduced to the simpler problem of code construction
for source resolvability. Specifically, we propose a MAC resolvability code
construction which involves a combination of multiple source resolvability
codes, used in a black box manner, and leverages randomness recycling
implemented via distributed hashing and block-Markov coding. Since explicit
source resolvability codes are known, our results also yield the first explicit
coding schemes that achieve the entire MAC resolvability region for any
discrete memoryless multiple access channel with binary input alphabets.
