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, zeros and ones only.

Analog

Analog system is a system in which the input and/or output is actual analog information and calculations occur on 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 an old fashion 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.

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 an example of an analog input and a discrete output. Using analog inputs, it determines which gear-set in a limited choice range to use to deliver power to the drive wheels.

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.

Digital - binary

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 sampled and represented as numeric approximation of the real value.

In a similar manor, a problem's algorithm, is expressed in a combination of hardware circuits and program sequences.

By applying an algorithm to the sampled 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 sampled and represented as approximate values in a valid range, the digital computer can apply the appropriate 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 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 computation.

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

Hybrid implementation.

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.

Most modern computation 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 as 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.

Analog TV delivered an image in real time.