The increasing demand for portable spectral analysis has driven the development of miniaturized spectrometers. Computational spectrometers, based on algorithmic reconstruction, are a potential solution to meet this demand. We report on the design and implementation of an integrated computational spectrometer on a silicon-on-insulator (SOI) substrate. The device is based on a 5-stage binary tree of cascaded silicon add-drop micro-ring resonators (MRRs). One of the 32 branches serves as the reference channel. Each of the other 31 branches has 4 cascaded MRRs with arbitrary coupling coefficients, cavity perimeters, and center distances. By using add-drop MRRs, we have 62 filter channels with 31 branches. It has no intrinsic structural reflection and scattering losses other than the excess loss in the 1 × 2 splitters and the waveguide propagation loss. The chip has a footprint of 1.5 mm2 and a resolution of 0.11 nm in the C-band. Broadband spectrum reconstruction with bandwidth >10 nm is also demonstrated.