To realize a real-time interactive holographic three-dimensional (3D) display system, we synthesize a set of 24 full high-definition (HD) binary computer-generated holograms (CGHs) based on a 3D fast-Fourier-transform-based approach. These 24 CGHs are streamed into a digital micromirror device (DMD) as a single 24-bit image at 60 Hz: 1440 CGHs are synthesized in less than a second. Continual updates of the CGHs displayed on the DMD and synchronization with a rotating mirror enlarges the horizontal viewing zone to 360° using a time-division approach. We successfully demonstrate interactive manipulation, such as object rotation, rendering mode switching, and threshold value alteration, for a medical dataset of a human head obtained by X-ray computed tomography.