In this paper, we propose new algorithms for computing the Discrete Hartley and the Discrete Cosine Transform. The algorithms are based on iterative applications of the mod)fied small n algorithms of DFT. The one dimensional transforms are mapped into two dimensions first and then implemented on two dimensional systolic arrays. Pipelined bit serial architectures operating on left to right LSB to MSB binary arithmetic is the basis of the hardware design. Different hardware schemes for implementing these transforms are studied. We show that our schemes achieve a substantial speed-up over existing schemes.