We have discussed the fact that the design of a digital circuit starts with the purpose of the circuit—what is the circuit to do? This involves stating the problem in a form that can be approached digitally (certainly not all purposes can be stated in this way!), which means defining input variables in such a way that all of the possible situations can be expressed as true or false values of the input variables. Then the output of the circuit must be defined such that all possible results can be expressed as a true or false output.
Once the definition phase of the circuit design is complete, the truth table for the system must be constructed. This simply means specifying all possible combinations of the inputs (that is, specifying the “universe” of input values—this will involve 2c rows in the truth table, where c is the number of components or inputs to the system) along with the truth-value of the output for each combination of inputs.
After the truth table has been constructed the minterms can be written out for each row having an output of 1. The minterms can then be combined in an OR gate to write out the full Boolean algebra expression for the truth table. This expression can then be used to draw the circuit diagram (as was done in the previous example).
The following example illustrates this process.
While the introduction to digital electronics that we have worked through is certainly very rudimentary, it nonetheless exposes us to the type of thinking behind the design of digital circuits. (Real digital circuit design can get quite complicated, but the circuits that we will deal with will be necessarily simple....) If you can follow through (or even anticipate!) the solution to the next example and work through the homework solutions then you have come a long way in this quick (4-lecture!) introduction to digital circuits!