Catalyzes the NAD-dependent reversible oxidation of erythritol and L-threitol. Involved in the degradation pathways of erythritol and L-threitol, that allow M.smegmatis to grow on these compounds as the sole carbon source. erythritol + NAD(+) = D-erythrulose + H(+) + NADH L-threitol + NAD(+) = H(+) + L-erythrulose + NADH Binds 2 Zn(2+) ions per subunit. kcat is 10.2 sec(-1) with L-threitol as substrate. kcat is 8.46 sec(-1) with erythritol as substrate. kcat is 8.73 sec(-1) with L-arabitol as substrate. kcat is 8.20 sec(-1) with xylitol as substrate. kcat is 6.56 sec(-1) with ribitol as substrate. kcat is 9.88 sec(-1) with D-erythrulose as substrate. kcat is 13.3 sec(-1) with L-erythrulose as substrate. kcat is 19.3 sec(-1) with D-xylulose as substrate. kcat is 7.75 sec(-1) with L-xylulose as substrate. kcat is 21.0 sec(-1) with ribulose as substrate. Carbohydrate metabolism; erythritol degradation. Carbohydrate metabolism; L-threitol degradation. Up-regulated during growth on erythritol, D-threitol or L-threitol relative to growth on glycerol. Complete loss of the ability to grow on erythritol or on L-threitol. Belongs to the zinc-containing alcohol dehydrogenase family.