Cognitive orthogonal frequency division multiplexing (C-OFDM) is an extremely promising technique for achieving high transmission capacity in the next generation cellular and wireless local area network (WLAN) systems with limited spectrum resources. Since the greedy bit allocation algorithm is the optimal method for single user, however, in the case of plenty of sub-carriers and bits to be distributed, the computational complexity will be extraordinarily unacceptable. This paper presents a new bit and power allocation scheme for C-OFDM systems based on the margin adaptive (MA) principle in which the overall transmission power is minimized by constraining the fixed data rate and bit error rate. The presented bit allocation algorithm is derived from geometric progression of the additional transmission power required by the sub-carriers and the arithmetic-geometric means inequality. Consequently, compared with the algorithm existing now, this algorithm has a simple procedure and low computational complexity. Simulation results show that the proposed algorithm is superior to the traditional algorithm, while reducing the computational complexity from exponential to linear in the number of sub-carriers.