Introduction to Logic Circuits & Logic Design with VHDL

We often hear that we live in a digital age. This refers to the massive adoption of computer systems within every aspect of our lives from smart phones to automobiles to household appliances. This statement also refers to the transformation that has occurred to our telecommunications infrastructure that now transmits voice, video, and data using 1’s and 0’s. There are a variety of reasons that digital systems have become so prevalent in our lives. In order to understand these reasons, it is good to start with an understanding of what a digital system is and how it compares to its counterpart, the analog system. The goal of this chapter is to provide an understanding of the basic principles of analog and digital systems.

Logic circuits are used to generate and transmit 1s and 0s to compute and convey information. This two-valued number system is called binary. As presented earlier, there are many advantages of using a binary system; however, the human brain has been taught to count, label, and measure using the decimal number system. The decimal number system contains 10 unique symbols (0 → 9) commonly referred to as the Arabic numerals. Each of these symbols is assigned a relative magnitude to the other symbols. For example, 0 is less than 1, 1 is less than 2, etc. It is often conjectured that the 10-symbol number system that we humans use is due to the availability of our ten fingers (or digits) to visualize counting up to 10. Regardless, our brains are trained to think of the real world in terms of a decimal system. In order to bridge the gap between the way our brains think (decimal) and how we build our computers (binary), we need to understand the basics of number systems. This includes the formal definition of a positional number system and how it can be extended to accommodate any arbitrarily large (or small) value. This also includes how to convert between different number systems that contain different numbers of symbols. In this chapter, we cover four different number systems: decimal (10 symbols), binary (2 symbols), octal (8 symbols), and hexadecimal (16 symbols). The study of decimal and binary is obvious as they represent how our brains interpret the physical world (decimal) and how our computers work (binary). Hexadecimal is studied because it is a useful means to represent large sets of binary values using a manageable number of symbols. Octal is rarely used but is studied as an example of how the formalization of the number systems can be applied to all systems regardless of the number of symbols they contain. This chapter also discusses how to perform basic arithmetic in the binary number system and represent negative numbers. The goal of this chapter is to provide an understanding of the basic principles of binary number systems.

Now we turn our attention to the physical circuitry and electrical quantities that are used to represent and operate on the binary codes 1 and 0. In this chapter we begin by looking at how logic circuits are described and introduce the basic set of gates used for all digital logic operations. We then look at the underlying circuitry that implements the basic gates including digital signaling and how voltages are used to represent 1s and 0s. We then look at interfacing between two digital circuits and how to ensure that when one circuit sends a binary code, the receiving circuit is able to determine which code was sent. Logic families are then introduced and the details of how basic gates are implemented at the switch level are presented. Finally, interfacing considerations are covered for the most common types of digital loads (i.e., other gates, resistors, and LEDs). The goal of this chapter is to provide an understanding of the basic electrical operation of digital circuits.

In this chapter we cover the techniques to synthesize, analyze, and manipulate logic functions. The purpose of these techniques is to ultimately create a logic circuit using the basic gates described in Chap. 3 from a truth table or word description. This process is called combinational logic design. Combinational logic refers to circuits where the output depends on the present value of the inputs. This simple definition implies that there is no storage capability in the circuitry and a change on the input immediately impacts the output. To begin, we first define the rules of Boolean algebra, which provide the framework for the legal operations and manipulations that can be taken on a two-valued number system (i.e., a binary system). We then explore a variety of logic design and manipulation techniques. These techniques allow us to directly create a logic circuit from a truth table and then to manipulate it to either reduce the number of gates necessary in the circuit or to convert the logic circuit into equivalent forms using alternate gates. The goal of this chapter is to provide an understanding of the basic principles of combinational logic design.

Based on the material presented in Chap. 4, there are a few observations about logic design that are apparent. First, the size of logic circuitry can scale quickly to the point where it is difficult to design by hand. Second, the process of moving from a high-level description of how a circuit works (e.g., a truth table) to a form that is ready to be implemented with real circuitry (e.g., a minimized logic diagram) is straightforward and well defined. Both of these observations motivate the use of computer-aided design (CAD) tools to accomplish logic design. This chapter introduces hardware description languages (HDLs) as a means to describe digital circuitry using a text-based language. HDLs provide a means to describe large digital systems without the need for schematics, which can become impractical in very large designs. HDLs have evolved to support logic simulation at different levels of abstraction. This provides designers the ability to begin designing and verifying functionality of large systems at a high level of abstraction and postpone the details of the circuit implementation until later in the design cycle. This enables a top-down design approach that is scalable across different logic families. HDLs have also evolved to support automated synthesis, which allows the CAD tools to take a functional description of a system (e.g., a truth table) and automatically create the gate-level circuitry to be implemented in real hardware. This allows designers to focus their attention on designing the behavior of a system and not spend as much time performing the formal logic synthesis steps that were presented in Chap. 4. The intent of this chapter is to introduce HDLs and their use in the modern digital design flow. This chapter covers the basics of designing combinational logic in an HDL and also hierarchical design. The more advanced concepts of HDLs such as sequential logic design, high-level abstraction, and adding functionality to an HDL through additional libraries and packages are covered later so that the reader can get started quickly using HDLs to gain experience with the languages and design flow.

This chapter introduces a group of combinational logic building blocks that are commonly used in digital design. As we move into systems that are larger than individual gates, there are naming conventions that are used to describe the size of the logic. Table 6.1 gives these naming conventions. In this chapter we look at medium-scale integrated circuit (MSI) logic. Each of these building blocks can be implemented using the combinational logic design steps covered in Chaps. 4 and 5. The goal of this chapter is to provide an understanding of the basic principles of MSI logic.

In Chap. 5 VHDL was presented as a way to describe the behavior of concurrent systems. The modeling techniques presented were appropriate for combinational logic because these types of circuits have outputs dependent only on the current values of their inputs. This means a model that continuously performs signal assignments provides an accurate model of this circuit behavior. In Chap. 7 sequential logic storage devices were presented that did not continuously update their outputs based on the instantaneous values of their inputs. Instead, sequential storage devices only update their outputs based upon an event, most often the edge of a clock signal. The modeling techniques presented in Chap. 5 are unable to accurately describe this type of behavior. In this chapter we describe the VHDL constructs to model signal assignments that are triggered by an event in order to accurately model sequential logic. We can then use these techniques to describe more complex sequential logic circuits such as finite-state machines and register transfer-level systems. This chapter also presents how to create test benches and looks at commonly used packages that increase the capability and accuracy with which VHDL can model modern systems. The goal of this chapter is to give an understanding of the full capability of hardware description languages.

In this chapter, we look at modeling sequential logic using the more sophisticated behavioral modeling techniques presented in Chap. 8. We begin by looking at modeling sequential storage devices. Next, we look at the behavioral modeling of finite-state machines. Finally, we look at register transfer level, or RTL modeling. The goal of this chapter is to provide an understanding of how hardware description languages can be used to create behavioral models of synchronous digital systems

This chapter introduces the basic concepts, terminology, and roles of memory in digital systems. The material presented here will not delve into the details of the device physics or low-level theory of operation. Instead, the intent of this chapter is to give a general overview of memory technology and its use in computer systems in addition to how to model memory in VHDL. The goal of this chapter is to give an understanding of the basic principles of semiconductor-based memory systems.

This chapter provides an overview of programmable logic devices (PLDs). The term PLD is used as a generic description for any circuit that can be programmed to implement digital logic. The technology and architectures of PLDs have advanced over time. A historical perspective is given on how the first programmable devices evolved into the programmable technologies that are prevalent today. The goal of this chapter is to provide a basic understanding of the principles of programmable logic devices.

This chapter presents the design and timing considerations of circuits to perform basic arithmetic operations including addition, subtraction, multiplication, and division. A discussion is also presented on how to model arithmetic circuits in VHDL. The goal of this chapter is to provide an understanding of the basic principles of binary arithmetic circuits.

One of the most common digital systems in use today is the computer. A computer accomplishes tasks through an architecture that uses both hardware and software. The hardware in a computer consists of many of the elements that we have covered so far. These include registers, arithmetic and logic circuits, finite-state machines, and memory. What makes a computer so useful is that the hardware is designed to accomplish a predetermined set of instructions. These instructions are relatively simple, such as moving data between memory and a register or performing arithmetic on two numbers. The instructions are comprised of binary codes that are stored in a memory device and represent the sequence of operations that the hardware will perform to accomplish a task. This sequence of instructions is called a computer program. What makes this architecture so useful is that the preexisting hardware can be programmed to perform an almost unlimited number of tasks by simply defining the sequence of instructions to be executed. The process of designing the sequence of instructions, or program, is called software development or software engineering.