In this paper, a fully digital low power Impulse Radio-Ultra Wide Band (IR-UWB) transmitter is proposed with low circuit complexity. The proposed circuit uses Random Selection (RS) algorithm for pulse shaping. The RS Algorithm is adopted for effectively combining the first fifteen derivatives of the Gaussian pulses in order to satisfy the Federal Communications Commission (FCC) emission mask at all frequencies. Each pulse is generated using a Fine Delay Element (FDE), Digital Pulse Combiner (DPC), buffers and Pulse Shape Controller (PSC). The circuit structure of a Fine Delay Element (FDE) used for generating delays is modified in order to reduce the power consumption. Digital Pulse Combining (DPC) technique is used to generate pulses of duration of 50 to 500 ps.