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# Digital Systems: Principles and Applications

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Nguyễn Gia Hào

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Parts of the text that use electronics terms can be skipped without adversely affecting the understanding of the logic principles. The HDL material can be skipped entirely without affecting the continuity of the text. Sections of the text that cover the special aspects of a language are clearly marked with a color bar in the margin.

Problems for which solutions are printed at the back of the text or on the website (http://www.pearsonhighered.com/ . careersresources/) are marked with an asterisk (see Figure P1). The answers to the tasks marked with an asterisk can be found in the background of the text. An IC index is provided at the back of the book to help readers find material on any IC cited or used in the text.

Describing logic

Combinational

Digital Arithmetic

Counters and

8-16 Mixed Voltage Interconnection 614 Low Voltage Outputs Driving High Voltage Loads 614 High Voltage Outputs Driving Low Voltage 614 Loads.

MSi logic Circuits 638

Digital System

Memory Devices 866

Programmable logic Device

RJT To my wife and best friend, Kris, who has sacrificed the most

## NSW To my expanding family, Marita, David, Ryan, Christy,

All digital systems in the world are built from a surprisingly small number of basic circuits or building blocks. A state marked with 1 is usually represented by a HIGH voltage and the value of this voltage depends on the system technology. A decimal point is used to separate whole and partial parts of a number.

All the previous statements about the decimal system are equally applicable to the binary system. This has been a brief introduction to the binary number system and its relationship to the decimal system. The measurements do not accurately represent the actual value at the time it is sampled due to the limitations of the measuring device (ten degree increments).

### And 1-3

Create a good label (name) for each signal described below:. a)*A sensor outputs a LOW when the elevator door is closed (b) A street light sensor outputs a HIGH when it detects daylight (c)*A passenger seat sensor goes LOW when the seat is empty (d) A temperature sensor goes HIGH when the radiator fluid is chalky -.

### And 1-5

Which of the following are analog quantities and which are digital. a) Width of a piece of wood. Which of the following will increase/decrease the quality of the digital signal. a) Extending the time between samples. Convert a number from one number system (decimal, binary, hexadecimal) to its equivalent in one of the other number systems.

The binary number system is the most important one in digital systems, but several others are also important. As you will see, it is not easy to simply look at a large binary number and convert it to its equivalent decimal value. Any binary number can be converted to its decimal equivalent simply by adding the weights of the various positions in the binary number that contain a 1.

And 2-2

### And 2-9

A transmitter connects to a code group to allow the receiver to detect. f) The code is the most common alphanumeric code used in computer systems. g) is often used as a convenient way to represent large binary numbers. h). The Or operation is the first of the three basic Boolean operations to be learned. What is the output state of the four-input circuit shown in Figure 3-1(c) when all inputs except B are 1.

The output of an AND gate is equal to the product of the AND logic inputs; that is, x = AB. The output of the INVERTER in Figure 3-11 is connected to the input of another INVERTER. The output of the AND gate in Figure 3-7 is connected to the INVERTER input.

The OR gate operates on its inputs so that its output is the OR sum of the inputs. The truth table in Figure 3-19(c) shows that the NOR gate output is the exact inverse of the OR gate output for all possible input conditions. The truth table in Figure 3-22(c) shows that the NAND gate output is the exact inverse of the AND gate for all possible input conditions.

The left side of the equation can be thought of as the output of a NOR gate whose inputs are x and y. The left side of the equation can be implemented by a NAND gate with inputs x and y. Note that this says that the output only goes to active state when all inputs are in their active state.

This says that the output will be in its active state when any of the inputs is in its active state. Write the interpretation of the operation performed by the standard NOR gate symbol in Figure 3-33. What will the output level be in Figure 3-38(b) when all inputs are asserted.

## OutcOmes

The tool we recommend is from Altera Corporation, one of the largest digital circuit suppliers in the world. Computer programs were developed to take the VHDL language files and simulate the operation of the circuits. Altera was one of the first companies to introduce electronically reconfigurable logic devices.

Computers work by following a laundry list of tasks (i.e., instructions or "the program"), all of which must be performed in order. The role of the hardware description language is to provide the designer with a concise and convenient way to describe the operation of the circuit in a format that a PC can process and easily store. The inputs and outputs (sometimes called gates) must be named and defined according to the nature of the gate.

Something must enclose the circuit we are trying to describe, just as a block diagram encloses everything that makes up that part of the design. The sequence of instructions describing the operation of the AHDL circuit is located in the logical portion between the keywords BEGIN and END. In this example, the operation of the hardware is described by a very simple Boolean algebra equation that states that the output (y) is assigned 1=2 to the logic level produced by a AND b.

Something must encompass the circuit we are trying to describe, just as a block diagram encompasses everything that makes up that part of the design. In Hardware In many implementations, signal points must be defined "inside" the circuit block. In HDL, these nodes (signals) are not defined by inputs and outputs, but in a section that describes the operation of the block.

Typing two consecutive dashes allows the designer to write information from that point to the end of the line.

### And 3-14

The circuit of Figure 3-55 is assumed to be a simple digital combination latch whose output will generate an active-LOW UNLOCK signal for only one combination of inputs. a)*Modify the circuit diagram so that it more effectively represents the operation of the circuit. Use the new circuit diagram to determine the input combination that will activate the output. Do this by returning from the exit using the information provided by the gate symbols, as was done in Examples 3-22 and 3-23.

Compare the results with the truth table obtained in Exercise 3-19. a) Determine the input conditions required to activate output Z in Figure 3-37(b). Modify the circuit diagram to reflect this, and then use the modified diagram to determine the input conditions required to activate the alarm. Determine the input conditions necessary to switch the output in Figure 3-59 to the active state.

Use the results of Problem 3-40 to obtain the complete truth table for the circuit of Figure 3-59. A positive pulse lasting 100 ns is applied to the input. a) Draw the input and output waveforms. The first element that appears at the top of an HDL list is the functional description. f) An object's type indicates whether it is an input or an output. g).

Here the light is an LED that will be ON (conducting) when the NOR gate output is LOW. Then verify that the circuit operates as a two-way switch using switches A and B. In Chapter 4 you will learn how to design circuits like this to produce a given ratio of input to output.). Label the output signals (horizontal lines) from the connection matrix (from top row to bottom row) as follows: AAABADHE.

Modify the circuit so that the microprocessor must provide the address code 4A16 to activate the LCD.

AHdl

### AHdl

• ABC + ABC

Each of the AND gates shown generates an output that is HIGH only for one given input condition and the output is LOW for all other conditions. So we can use the ABC term to pair with any of the other terms. For each case in the truth table, we have indicated the decimal equivalent of the binary number represented by the ABCD combination.

The truth table is shown in Table 4-3. The S output will be a logic 1 when P = 0 because this indicates that there is no paper in the input tray. Similarly, the condition A = 1, B = 1 in the truth table corresponds to the AB square of the K map. Variables that are the same for all squares in the loop must appear in the final expression.

Every time we don't care, we have to decide which x to change to 0 and which to 1 to produce the best K-map looping (i.e. simplest expression). This symbol is assumed to contain all of the logic in the XOR circuit and therefore has the same logic expression and truth table. It should be obvious that the output of the XNOR circuit is the exact inverse of the output of the XOR circuit.

An abbreviated way of expressing the output expression of the XNOR is x = A∙B. which is simply the inverse of the XOR operation. This will often lead to the use of XOR or XNOR gates in the final circuit implementation. Use Boolean algebra to prove that the XNOR output expression is the exact inverse of the XOR output expression.

Each of the basic logic gates can be used to control the passage of a logic input signal to the output. Conversely, when the inverting gates (NAND, NOR) are enabled, the output will be the exact inverse of the A signal. Sometimes the output will oscillate due to the noise picked up by the floating input.

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