We have study the fundamentals of Digital circuits. Primary we have studied the mathematics of Binary numbers also called as Boolean algebra and how to implement this Boolean algebra in digital circuits with the help of Logic gates. Then we have done a detailed study of how to make K-maps from the truth tables of SOP equations and how to simplify K-maps to obtain the most simplified combinatorial logic circuits. A digital system, which utilizes Binary numbers, has only two possible states. But for some specific applications we require an extra state called High Z state, here comes the ideas/concepts of Tristate Logic gates. Till now whatever combinatorial logic circuits considered were asynchronous circuits. In the next section we have studied Sequential circuits as Flip Flops, Counters and Shift registers which works in synchronism with the clock pulse. Next we have learned how transistors are utilized for realization of digital circuit's viz. TTL and CMOS circuits. We have also investigated different type of memories in the computers: non-volatile, volatile, Read only and random access memories. At last, we tried to understand the main function of MODEMs and have also studied simple ADC and DAC circuits.