Brain-Computer Interface (BCI) plays a major role in current technologies such as rehabilitation, control of devices, and various medical applications. BCI or brain-machine interface provides direct communication between a brain signal and an external device. In this paperwork, a detailed survey was carried out with the design of single-channel EEG system for various applications. Also, this paper mainly focused on the development of single-channel electroencephalography (EEG) signal acquisition system which includes a preamplifier, bandpass filter, post-amplifier and level shifter circuits. The design of the preamplifier and post-amplifier circuit was carried out by integrated circuits (IC) such as instrumentation amplifier IN128P and bandpass filter with the help of low power operational amplifier LM324. The developed single-channel acquisition board was tested by acquiring an electrooculogram (EOG) signal with closed and opened eye conditions. The acquired signal is displayed and stored in the computer with the help of the HBM-DAQ unit.