The line projection with a lattice of points and the strip projection with a lattice of cells are popularly used in modeling the raw detector reading in discrete tomography (DT). In the strip-based projection model for a 2D rectangular region, the projection equations are formulated according to the fractional areas of the intersection of each strip-shaped beam and the rectangular grid of an image. We propose, in this paper, a scheme to formulate a real system of linear equations for the strip-based projection model and to convert it into a binary linear system. Thus all the existing reconstruction algorithms for the line-based projection model in DT can be accordingly adapted. Numerical examples are given to illustrate our algorithm.