We present an area efficient method and field programmable gate array (FPGA) realization for two common operations in robotics, namely, the following: (1) rotating a vector in 2D and (2) aligning a vector in the plane with a specific axis. It is based on a new coordinate rotation digital computer (CORDIC) algorithm that is designed to work with a small set of elementary angles. Unlike conventional CORDIC, the proposed algorithm does not require a ROM and a full-fledged barrel shifter. The proposed CORDIC algorithm is used to design hardware efficient solutions for two mobile robotic tasks in an indoor environment without employing division and floating-point calculations. Experiments with a sole low end FPGA based robot in static as well as dynamic environments validate the power of the approach.