Different multiplication algorithms have different performance characteristics. Some are good at speed while others consume less area when implemented on hardware, like Field Programmable Gate Array (FPGA)-the advanced implementation technology for DSP systems. The eminent parallel and sequential multiplication algorithms include Shift and Add, Wallace Tree, Booth, and Array. The multiplier optimization attempts have also been reported in adders used for partial product addition. In this paper, analogous to conventional multipliers, two new multiplication algorithms implemented on FPGA are shown and compared with conventional algorithms as stand-alone and by using them in the implementation of FIR filters and adaptive channel equalizer using the LMS algorithm. The work is carried out on Spartan-6 FPG that may be extended for any type of FPGA. Results are compared in terms of resource utilization, power consumption, and maximum achieved frequency. The results show that for a small length of coefficients like 3-bit, the proposed algorithms work very well in terms of achieved frequency, consumed power, and even resource utilization. Whilst for the length greater than 3-bit, the Pipelined multiplier is much better in frequency than the proposed and conventional ones, and the Booth multiplier consumes fewer resources in terms of lookup tables.