3.4 Digital Components
Upon opening a computer and looking inside, one would realize that there is a lot to know about all of the digital components that make up the system. Every computer is built using collections of gates that are all connected by way of wires acting as signal gateways. These collections of gates are often quite standard, resulting in a set of building blocks that can be used to build the entire computer system. Surprisingly, these building blocks are all constructed using the basic AND, OR, and NOT operations. In the next few sections, we discuss digital circuits, their relationship to Boolean algebra, the standard building blocks, and examples of the two different categories, combinational logic and sequential logic, into which these building blocks can be placed.
3.4.1 Digital Circuits and Their Relationship to Boolean Algebra
What is the connection between Boolean functions and digital circuits? We have seen that a simple Boolean operation (such as AND or OR) can be represented by a simple logic gate. More complex Boolean expressions can be represented as combinations of AND, OR, and NOT gates, resulting in a logic diagram that describes the entire expression. This logic diagram represents the physical implementation of the given expression, or the actual digital circuit. Consider the function 
(which we looked at earlier). Figure 3.9 represents a logic diagram that implements this function.
We can build logic diagrams (which in turn lead to digital circuits) for any Boolean expression.
Boolean algebra allows us to analyze and design digital circuits. Because of the relationship between Boolean algebra and logic diagrams, we simplify our circuit by simplifying our Boolean expression. Digital circuits are implemented with gates, but gates and logic diagrams are not the most convenient forms for representing digital circuits during the design phase. Boolean expressions are much better to use during this phase because they are easier to manipulate and simplify.
The complexity of the expression representing a Boolean function has a direct impact on the complexity of the resulting digital circuit; the more complex the expression, the more complex the resulting circuit. We should point out that we do not typically simplify our circuits using Boolean identities; we have already seen that this can sometimes be quite difficult and time consuming. Instead, designers use a more automated method to do this. This method involves the use of Karnaugh maps (or Kmaps). The interested reader is referred to the focus section following this chapter to learn how Kmaps help to simplify digital circuits.
3.4.2 Integrated Circuits
Computers are composed of various digital components, connected by wires. Like a good program, the actual hardware of a computer uses collections of gates to create larger modules, which, in turn, are used to implement various functions. The number of gates required to create these "building blocks" depends on the technology being used. Because the circuit technology is beyond the scope of this text, the reader is referred to the reading list at the end of this chapter for more information on circuit technology.
Typically, gates are not sold individually; they are sold in units called integrated circuits (ICs). A chip (a small silicon semiconductor crystal) is a small electronic device consisting of the necessary electronic components (transistors, resistors, and capacitors) to implement various gates. As described in Chapter 1, components are etched directly on the chip, allowing them to be smaller and to require less power for operation than their discrete component counterparts. This chip is then mounted in a ceramic or plastic container with external pins. The necessary connections are welded from the chip to the external pins to form an IC. The first ICs contained very few transistors. As we learned in Chapter 1, the first ICs were called SSI chips and contained up to 100 electronic components per chip. We now have ULSI (ultra large-scale integration) with more than 1 million electronic components per chip. Figure 3.10 illustrates a simple SSI IC.
