Memristor, also known as memory resistor, is considered as the fourth passive electronic element expressing the relationship between magnetic flux and electric charge. One of the most important features of the memristor is that it has low power consumption. Minimizing power consumption is an important issue in the electronic circuits. However, the fact that the memristor element was not yet fully manufactured has led researchers to design memristor-like emulator circuits. These circuits, which approximate the memristor properties, are realized by combining the other existing electronic elements. In this paper, a basic NAND logic gate is considered and the change in power consumption when using a memristor instead of the standard resistor in the gate circuit is examined. For this purpose, the NAND logic circuit was constituted for four different memristor emulators, and the power consumption values of these circuits were obtained by simulation and experiments. These values are compared with the power consumption values of NAND circuits obtained by using standard resistors equivalent to the memristor resistance. The results clearly show that the memristor gate circuits reduce power consumption compared to standard resistive gate circuits.