Chapter 1 Number Systems and Codes William Kleitz Digital Electronics with VHDL, Quartus® II Version Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey.

Download Report

Transcript Chapter 1 Number Systems and Codes William Kleitz Digital Electronics with VHDL, Quartus® II Version Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey.

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Chapter 1 Digital Versus Analog

• Digital – ON and OFF – 0 and 1 • Analog – continuously varying – temperature, pressure, velocity • See Figure 1-1

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Figure 1-1

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Digital Representations of Analog Quantities

• Audio Recording – CD or DAT • Conversions – digital-to-analog – analog voltage to 8-bit Digital equivalent • See Figure 1-2 and 1-3

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Figure 1-2

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Decimal Numbering System (Base 10)

• 10 different possible digits • Least significant position – rightmost • Most significant digit – leftmost • Weighting factor of 10

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Binary Numbering System (Base 2)

• Only 0 and 1 • Weighting factor of 2 • Conversion techniques – digit times weighting factor – successive division

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Decimal-to-Binary Conversion

• Subtracting weighting factors • Successive division • Least Significant Bit (LSB) • Most Significant Bit (MSB)

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Octal Numbering System (Base 8)

• Allowable digits – 0,1,2,3,4,5,6,7 • Weighting factor of 8

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Octal Conversions

• Binary to Octal – group binary positions in groups of three – write the octal equivalent • Octal to Binary – reverse the process • Octal to Decimal – multiply by weighting factors • Decimal to Octal – successive division

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Hexadecimal Numbering System (Base 16)

• 4-bit groupings • See Table 1-3 • Two hex digits are used to represent 8 bits – a byte – 4 bits are a nibble

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Hexadecimal Conversions

• Binary to Hexadecimal – group the binary in groups of four – write the equivalent hex digit • Hexadecimal to Binary – reverse the process

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Hexadecimal Conversions

• Hexadecimal to Decimal – multiply by weighting factors • Decimal to Hexadecimal – successive division

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Binary-Coded-Decimal System BCD

• Each of the 10 decimal digits has a 4-bit binary code • Conversion – convert each decimal digit to its 4-bit binary code – BCD to Decimal - reverse the process

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Comparison of Numbering Systems

• See Table 1-4

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

The ASCII Code

• Represents alphanumeric data • Uses 7 bits • 128 different code combinations • See Table 1-5 – 3-bit group is most significant – 4-bit group is least significant

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Summary

• Numerical quantities occur in analog form but must be converted to digital form to be used by computers or digital circuitry.

• The binary numbering system is used in digital systems because the 1’s and 0’s are easily represented by ON or OFF transistors, which output 0V for 0 and 5V for 1.

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Summary

• Any number system can be converted to decimal by multiplying each digit by its weighting factor.

• The weighting factor for the least significant digit in any number system is always 1.

• Binary numbers can be converted to octal by forming groups of 3 bits and to hexadecimal by forming groups of 4 bits.

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Summary

• The successive division procedure can be used to convert from decimal to binary, octal or hexadecimal • The binary-coded-decimal system uses groups of 4 bits to drive decimal displays such as those in a calculator.

• ASCII is used by computers to represent all letters, numbers and symbols in digital form.

William Kleitz

Digital Electronics with VHDL, Quartus® II Version

Chapter 1 Number Systems and Codes William Kleitz Digital Electronics with VHDL, Quartus® II Version Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey.

Transcript Chapter 1 Number Systems and Codes William Kleitz Digital Electronics with VHDL, Quartus® II Version Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey.

Chapter 1

Digital Versus Analog

Digital Representations of Analog Quantities

Decimal Numbering System (Base 10)

Binary Numbering System (Base 2)

Decimal-to-Binary Conversion

Octal Numbering System (Base 8)

Octal Conversions

Hexadecimal Numbering System (Base 16)

Hexadecimal Conversions

Hexadecimal Conversions

Binary-Coded-Decimal System BCD

Comparison of Numbering Systems

The ASCII Code

Summary

Summary

Summary

Directory