While unbiased surveys observable from ground-based telescopes have previously been obtained towards several high mass protostars, very little exists on low mass protostars. To fill up this gap, we carried out a complete spectral survey of the bands at 3, 2, 1 and 0.8 mm towards the solar type protostar IRAS16293-2422. The observations covered about 200,GHz and were obtained with the IRAM-30m and JCMT-15m telescopes. Particular attention was devoted to the inter-calibration of the obtained spectra with previous observations. All the lines detected with more than 3 sigma and free from obvious blending effects were fitted with Gaussians to estimate their basic kinematic properties. More than 4000 lines were detected (with sigma geq 3) and identified, yielding a line density of approximatively 20 lines per GHz, comparable to previous surveys in massive hot cores. The vast majority (~2/3) of the lines are weak and due to complex organic molecules. The analysis of the profiles of more than 1000 lines belonging 70 species firmly establishes the presence of two distinct velocity components, associated with the two objects, A and B, forming the IRAS16293-2422 binary system. In the source A, the line widths of several species increase with the upper level energy of the transition, a behavior compatible with gas infalling towards a ~1 Mo object. The source B, which does not show this effect, might have a much lower central mass of ~0.1 Mo. The difference in the rest velocities of both objects is consistent with the hypothesis that the source B rotates around the source A. This spectral survey, although obtained with single-dish telescope with a low spatial resolution, allows to separate the emission from 2 different components, thanks to the large number of lines detected. The data of the survey are public and can be retrieved on the web site http://www-laog.obs.ujf-grenoble.fr/heberges/timasss.