What are the Parts of a Modem?
As it is an electronic device, there is a printed circuit inside the modem that holds the capacitors, resistors, transistors, amplifiers, regulators, flash memories, diodes, switches, and so on. For an overly technical view of the circuitry you can google a little and find very useful (and possibly overwhelming) results. For the purposes of this article, we will stick with the basic conceptual components of modems.
Modems have the parts to send and receive signals (digital and analog) and to convert them to one another. In an internal dial-up modem, sending and receiving is done by the connection of the telephone line and the signals are sent to the computer via the motherboard connection. In external modems, sending and receiving is done again by the telephone line connection and the signals are sent to the computer via the serial or USB port. In broadband modems (known as the DSL modems), the sending and receiving component is the same, however the signals are sent to the computer through the Ethernet or the USB connection (I recommend using one with an Ethernet connection). If the modem can transmit and receive data at the same time, it is called a “duplex" modem. If not, it is called a “simplex" modem.
In processing the signals, the modem has a flash memory that holds the operating system, which consists of the set of instructions on how to process the signals and transfer them to the connection – the connection being either the telephone line connection or the connection with the computer. Since we are talking on an “operating system", there is a central processing unit and memory.
Modulation and demodulation is done by separate parts – the modulator and the demodulator as you have guessed. Assuming that the data packets that arrive and sent from the computer can contain errors, there is also an error control module on the modem.