The very first designs that came about were analog designs, a Vacuum Tube amplifier is an example. Analog is the representation of data or physical parameter in an accurate and precise decimal number like + 72.182 mV. The greater the resolution required, the more demanding is the design for achieving high accuracy and low drift. Digital circuits have only two voltage levels, high and low, the third state of floating, Hi-Z or high impedance is only for multiplexing or sharing a bus. This is done so that devices dont drive into each other and it is also used in external port drivers.
As an analogy, see the conventional water tap as an analog control, an electric light ON-OFF switch as a digital control.
Even in digital, going from a low level say 0V to a high level say 5V is not instantaneous, the side of the square wave or the rising edge is not as straight as it looks. On zooming only the edge, you see that it is also an analog phenomena. The 'square wave' itself appears to be a summation of many sine waves, 'harmonics'. This is because nature is analog, the sine wave is analog, the movements of the planets or even the spin of electrons in an atom too. 
After the handheld Abacus calculator (low-power, durable, bio-degradable), Mechanical and electro-mechanical computers were made and studied, The very first electronic computers were Analog Computers using an opamp as a building block.
Then came huge Digital Computers, Later LSI and other Microelectronic Innovations have precipitated handheld computers. An iPod Touch has a Business-Scientific calculator and an Abacus as well.
The Rising edge of the square wave depends on the Transient Response of the devices, the slew rate and bandwidth too. Fast Op-Amps are required for many applications, in switching and also AC amplification. Beyond that, study goes into Power Electronics and RF-Microwave which are specialized extensions of Analog. Similarly study of Digital Circuits extends into Computers.
17:36 24-Oct-08
Anantha Narayan
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