We present results from the second-generation Energetic X-ray Imaging Telescope (EXITE2) observations of the black hole X-ray binary Cyg X-1 during the experiment's 1997 and 2001 flights. The EXITE2 phoswich [NaI(Tl)/CsI(Na)] detector is designed to image cosmic X-ray sources in the hard X-ray band by using the coded-aperture imaging technique from a high-altitude scientific balloon. The sky image reconstruction methodology used for EXITE2 is also discussed in detail. Background reduction (PSD rejection), subtractive flat-fielding, pixel shuffling, and image functions are introduced. During the observations from the EXITE2 1997 and 2001 flights, Cyg X-l is easily detected in the 37-237 keV energy range. During the 1997 observations, the spectrum is well fitted by a Comptonization model. The spectral signatures and the observed 100 keV flux, together with the RXTE ASM light curve, indicate that the source was in the typical low state during this observation. Evidence is seen for hard X-ray variability on timescales on the order of 10 minutes. During the 2001 flight the spectrum is best fit by an extended power law with no observable cutoff. This is possible evidence of a transition to the high state, which is indeed seen in the RXTE ASM light curve shortly after our observation.