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Chapter 1 Number Systems and Codes 1. Objectives  You should be able to: –Explain the difference between analog and digital. –Determine the weighting.

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Presentation on theme: "Chapter 1 Number Systems and Codes 1. Objectives  You should be able to: –Explain the difference between analog and digital. –Determine the weighting."— Presentation transcript:

1 Chapter 1 Number Systems and Codes 1

2 Objectives  You should be able to: –Explain the difference between analog and digital. –Determine the weighting of digit positions in decimal, binary, octal, and hexadecimal numbering systems. –Convert numbers among the four numbering systems. 2

3 Objectives  You should be able to: –Describe binary coded decimal (BCD) numbers. –Translate alphanumeric data to and from ASCII. 3

4 Digital versus Analog  Digital –ON and OFF –0 and 1  Analog –Continuously varying –Examples: temperature, pressure, velocity  See Figure 1-1 4

5 Figure 1-1 5

6 Discussion Points  Explain the difference between analog and digital signals.  Describe some applications for digital technology.  What are the benefits of using digital systems?  Are there any problems associated with digital systems? 6

7 Digital Representations of Analog Quantities  Audio Recording –CD, DAT, and MP3  Conversions –Digital-to-analog –Analog voltage to 8-bit Digital equivalent  See Figures 1-2 and 1-3 7

8 Figure 1-2 Figure 1-3 8

9 Why Digital systems are immune to analog noise 9

10 Decimal Numbering System (Base 10)  10 different possible digits  Least significant position –Rightmost  Most significant digit –Leftmost  Weighting factor of 10 10

11 Binary Numbering System (Base 2)  Only 0 and 1  Weighting factor of 2  Conversion techniques –Digit times weighting factor –Successive division 11

12 Decimal-to-Binary Conversion  Subtracting weighting factors  Successive division  Least Significant Bit (LSB)  Most Significant Bit (MSB) 12

13 Octal Numbering System (Base 8)  Allowable digits –0,1,2,3,4,5,6,7  Weighting factor of 8 13

14 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 14

15 Hexadecimal Numbering System (Base 16)  4-bit groupings  See Table 1-3 in your text  Two hex digits are used to represent 8 bits –A byte –4 bits are a nibble 15

16 Hexadecimal Conversions  Binary to hexadecimal –Group the binary in groups of four –Write the equivalent hex digit  Hexadecimal to binary –Reverse the process 16

17 Hexadecimal Conversions  Hexadecimal to decimal –Multiply by weighting factors  Decimal to hexadecimal –Successive division 17

18 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 18

19 Comparison of Numbering Systems  See Table 1-4 in your text 19

20 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 20

21 21

22 Applications of the Numbering Systems  Application

23 Applications of the Numbering Systems  Application 1-2 –A CD player is capable of converting 12 bit signals from a CD into equivalent analog values.  What are the largest and smallest hex values that can be used in this system?  How many different analog values can be represented? 23

24 Applications of the Numbering Systems  Application 1-3 –Typically, digital thermometers use BCD to drive their displays.  How many BCD bits are required to drive a 3 digit thermometer display?  What bits are sent to the display for 147 degrees? 24

25 Applications of the Numbering Systems  Application 1-4 –Most PC-compatible computer systems use a 20-bit address code to identify each of over 1 million memory locations.  How many hex characters are required to identify the address of each memory location?  What is the hex address of the 200 th memory location?  If 50 memory locations are used for data storage starting at location 000C8H, what is the location of the last data item? 25

26 Applications of the Numbering Systems  Application 1-5 –If the part number 651-M is stored in ASCII in a computer memory, list the binary contents of its memory locations. 26

27 Applications of the Numbering Systems  Application 1-6 –A programmer uses a debugging utility to find an error in a BASIC program. The utility shows the ASCII code as hex 474F Assume that the leftmost bit of each ASCII string is padded with a zero.  Translate the program segment that is displayed.  Try to determine what the error is. 27

28 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. 28

29 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. 29

30 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. 30


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