We investigate the X-ray number counts in the 1-2 Ms Chandra Deep Fields (CDFs) to determine the contributions of faint X-ray source populations to the extragalactic X-ray background (XRB). X-ray sources were separated into Active Galactic Nuclei (AGN), star-forming galaxies, and Galactic stars based on several criteria. We find that AGN continue to dominate the number counts in the 0.5-2.0 keV and 2-8 keV bands. At flux limits of ~2.5e-17 erg cm-2 s-1 (0.5-2.0 keV) and ~1.4e-16 erg cm-2 s-1 (2-8 keV), the overall AGN source densities are 7166 (+304/-292) and 4558 (+216/-207) sources deg-2, respectively; these are factors of ~10-20 higher than found in the deepest optical spectroscopic surveys. While still a minority, the number counts of star-forming galaxies climb steeply such that they eventually achieve source densities of 1727 (+187/-169) and 711 (+270/-202) sources deg-2 at the CDF 0.5-2.0 keV and 2-8 keV flux limits, respectively. Adopting recent XRB flux densities measurements, the CDFs resolve a total of 89.5% (+5.9%/-5.7%) and 86.9% (+6.6%/-6.3%) of the extragalactic 0.5-2.0 keV and 2-8 keV XRBs, respectively. Extrapolation of the number-count slopes can easily account for the entire 0.5-2.0 keV and 2-8 keV XRBs to within statistical errors. We also revisit the reported differences between the CDF-North and CDF-South number counts, finding that the two fields are consistent except for sources in the 2-8 keV band below F(2-8 keV)~1e-15 erg cm-2 s-1, where deviations gradually increase to ~3.9 sigma.
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