In this post we take a look at an example that illustrates the general principles that digital circuit designers employ in designing and implementing circuits. These principles increase productivity as well as robustness and they help reduce error.

Despite the world being analog, digital is still the go-to way for a large majority of chip designs. Why is this the case?

Digital is more convenient because it is an abstraction. There is no need to know how transistors work or to worry about currents and voltages.

Abstraction refers to the act of concealing details that do not matter for how a system is used. In the process of hiding the irrelevant details, digital designers abide by the principle of discipline; that is, they limit their design choices in such a way as to increase productivity. An example will be helpful in illustrating the above concepts. As a result, we look at defining logic levels.

Defining Logic Levels

Digital design deals with discrete values. However, underlying all the discrete values are continuous variables such as voltage and current. The continuous variables are mapped onto a discrete binary variable, thereby allowing a certain range of voltage values to be interpreted as a logical 1 while another range will represent a logical 0. The diagram below features the defining of logic levels.

In the diagram, we have associated the range of voltage values from 0 to VL with logical 0 and those from VH to V with logical 1. With this relation established, a component can then be abstracted and used while only keeping in mind that a certain voltage threshold leads to 1 and that some other leads to 0. The diagram below makes the idea concrete. The triangular component takes in some voltage value and outputs a voltage value that can be interpreted as 1 or 0.

However, before this abstraction, designers must meet the static discipline. Static discipline requires that if a digital circuit receives a logically valid input, then it will produce a logically valid output. In other words, people working on circuits will implement them so that input or output voltages only fall within the logical 1 or 0 zones. If, for some unintended reason, the input should fall within the forbidden zone, (the region between VL and VH, indicated in the first diagram), the circuit behaves unpredictably and should not be expected to work as specified.

Managing Complexity

In addition to abstraction and discipline, digital designers use the three ideas of hierarchy, modularity and regularity to break down large systems into smaller systems that are more manageable. Specifically, hierarchy calls for decomposing the system into its major components; then, these components are further subdivided into various modules. As a result, the system can be looked at as a hierarchy of components. The figure below illustrates this: the green complex system is broken down into its constituent parts colored orange, red and blue.

Modularity ensures that the components have a clearly defined function so that they can be assembled hierarchically into the bigger system without any unintended side effects. Last but not the least: regularity. It works at creating uniformity among the various modules. Regularity allows modules to be interchanged with those similarly specified. An analogy that may help here is one involving a door knob. When a knob breaks or no longer functions properly, one can simply go into a shop and purchase a similar knob as replacement; one need not throw away the whole door. In this sense, the malfunctioning knob is not the only one that could possibly fit the door. Likewise, the two modules depicted below, whose function is to add inputs of form A, B and C and produce outputs of the form Out 1 and Out 2, are interchangeable.

In conclusion, by limiting their design choices, digital circuit designers are able to avoid unnecessary details like the whole range of voltage values or the particular nature of noise. They define logic levels and then abstract the component; this increases productivity greatly. Moreover, designers exploit hierarchy, modularity and regularity in managing complex projects: they break down larger systems into smaller systems, build these smaller systems and then assemble these modules to get a solution to the complex project. All of these ideas help digital circuit designers design and build robust systems in a less time consuming and relatively very error proof way.