We present high angular resolution 1.3 mm and 850 um dust continuum data obtained with the Submillimeter Array toward 33 Class 0 protostars in nearby clouds (distance < 500 pc), which represents so far the largest survey toward protostellar binary/multiple systems. The median angular resolution in the survey is 2.5 arcsec, while the median linear resolution is approximately 600 AU. Compact dust continuum emission is observed from all sources in the sample. Twenty-one sources in the sample show signatures of binarity/multiplicity, with separations ranging from 50 to 5000 AU. The numbers of singles, binaries, triples, and quadruples in the sample are 12, 14, 5, and 2, respectively. The derived multiplicity frequency (MF) and companion star fraction (CSF) for Class 0 protostars are 0.64+/-0.08 and 0.91+/-0.05, respectively, with no correction for completeness. The derived MF and CSF in this survey are approximately two times higher than the values found in the binary surveys toward Class I YSOs, and approximately three (for MF) and four (for CSF) times larger than the values found among MS stars, with a similar range of separations. Furthermore, the observed fraction of high order multiple systems to binary systems in Class 0 protostars (0.50+/-0.09) is also larger than the fractions found in Class I YSOs (0.31+/-0.07) and MS stars (< 0.2). These results suggest that binary properties evolve as protostars evolve, as predicted by numerical simulations. The distribution of separations for Class 0 protostellar binary systems shows a general trend in which companion star fraction increases with decreasing companion separation. We find that 67%+/-8% of the protobinary systems have circumstellar mass ratios below 0.5, implying that unequal-mass systems are preferred in the process of binary star formation. We suggest an empirical sequential fragmentation picture for binary star formation.
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