While there may be several exotic ways to design a computational system, the most common types are either analog or binary

Analog systems vs. Digital (discrete binary)

Analog - a value that represents a measured sample of a continuously variable quantity. (paraphrased from wiktionary.org). Within an individual's vocal range, a tone of any frequency possible.

Discrete - having separate fixed value measurements. Integer (whole) numbers are values that are separated by a value of one or some multiple of it.

Binary - a discrete calculating system based on radix 2 counting, using zeros and ones only.

Analog system is a system in which the input and/or output is actual analog information and calculations occur over a continuous value range. Analog systems have the advantage of being very fast, often real time, and accurate to the limits of the system.

An example of an analog computer is broadcast radio. The human voice is converted to an analog electrical signal which in turn is used to modulate a radio frequency which can be transmitted many miles. Upon reception, the process is reversed, regenerating a close approximation of the original sound.

Although not usually viewed a computational system, the process of converting an audio signal to electrical and then radio wave and back using well defined rules is computational. Additionally, the ability to tune a radio to select different broadcast signals represents a computational input.

Another example of an analog computer is a continuous transmission. It takes throttle input, current speed, and work load to determine power delivered to the drive wheel.

Automobile transmissions are an example of an analog/discrete computational system. It takes both analog input, engine speed, and discrete input, either a computed gear range based on both current engine speed and axle speed or a manual override, and generates an analog power output to the drive train.

The major advantage of analog calculating systems is that they tend to run/calculate in real time on a continuous time-line.

The major disadvantage is that it is difficult to take a particular analog 'computer' and make it do something else. You can't use a radio to control the output of an automobile's power train.

A binary digital system is a system that uses only 2 values, 0 and 1, or on and off, at its atomic (simplest) bit level. Larger values are represented by grouping bits together. Any real world information is represented as numeric representation of the real value.

A problem's algorithm is expressed in a combination of hardware circuits and program sequences represented by specific digital values.

By applying an algorithm to the data, new information is calculated and the results are either stored or further processed to provide an understandable representation to the user.

Digital computers have the advantage of being very flexible. As long as the real world information can be represented as values in a valid range, the digital computer can apply appropriately arranged algorithm steps to arrive at a solution.

A downside to digital computing is that the real information has to be sampled via additional circuitry and processed by algorithms to obtain the digital representation. And, depending on the goal of the computation, the reverse may have to occur.

Another downside is that both the range and precision of data presentation is limited to provide efficient system design and computational speed. Improved precision introduces additional storage needs and computational work and costs.

Additionally, the sampling takes time and resources. Although with technological advances this issue is improving. Computation barely conceivable 30 years ago is now accomplished with hand-held devices very quickly.

As technology advances, improvements in speed and 'quality' of digital computation has made it a contender in areas that previously required use of analog computation.

Many modern computational tasks starts by taking analog data and 'sampling' to obtain a digital representation.

An example of this is television broadcast. Once a purely analog technology, cameras detected the level of red, blue, and green in the scene they were recording, converted each to a variable voltage which in turn was amplified and used to modulate a radio signal which was broadcast to the television receiver where the process was reversed to the point where the variable voltage would determine at any moment the brightness of the red, green, and blue pixels on the screen. The end user could provide additional filter inputs, volume, color, tint, contrast, etc. to the final expression of the transmitted data.

Analog TV delivered an image in very near real time.

Modern technology allows cameras to sample and convert an image to a digital stream of data. This data can then be manipulated, compressed, stored, and transmitted, either over digital or analog carriers and recovered at the receiving end.

Transmission is still possible in near real time. Additionally, archiving is much more efficient than it was in early broadcasting. And much of the technology used in the intermediate steps is used to transmit/store any variety of data.