1. An image forming system, comprising: a data conversion unit that thins out first image data configured by arranging dot data in matrix fashion and converts two-line data of the first image data into one-line data of second image data, the dot data representing either one of image forming dot data with which an image is to be formed and non-image forming dot data with which an image is to be not formed; and an image output unit that outputs an image obtained by reproducing the second image data converted by the data conversion unit, wherein the data conversion unit includes: a determination unit which divides the first image data into a dot block each of which includes two-row by two-column of dot data, and determines whether or not an array of dot data included in each dot block corresponds to a first or second array, wherein the first array includes two of the image forming dots in the first row and two of the non-image forming dots in the second row, and the second array includes two of the non-image forming dots in the first row and two of the image forming dots in the second row; and an output unit which, when the determination unit determines that the array in a dot block corresponds to the first array, outputs the image forming data and the non-image forming data in order as a part of one-line data of the second image data, when the determination unit determines that the array in a dot block corresponds to the second array, outputs the non-image forming data and the image forming data in order as a part of one-line data of the second image data, and when the determination unit determines that the array in a dot block does not correspond to the first array nor the second array, outputs dot data in the first row of the array as a part of one-line data of the second image data.