CHAPTER 1 - Number Systems, Codes and Applications

7/25/2019 CHAPTER 1 - Number Systems, Codes and Applications

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SE 3204COMPUTER ARCHITECTURE I


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TOPIC OUTLINE

1. Digital versus Analog2. Digital Representations of Analog Quantities3. Decimal Numbering System (Base 10)4. Binary Numbering System (Base 2)5. Decimal-to-Binary Conversion6. Octal Numbering System (Base 8)

7. Octal Conversions8. Hexadecimal Numbering System (Base 16)9. Hexadecimal Conversions10. Binary-Coded-Decimal System11. Comparison of Numbering Systems12.The ASCII Code13.Applications of the Numbering Systems


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LEARNING OUTCOMES

Upon completion of this chapter, you should be able to do the followin

Determine the weighting factor for each digit position in the decimal, binaroctal, and hexadecimal numbering systems.

Convert any number in one of the four number systems (decimal, binary, o

and hexadecimal) to its equivalent value in any of the remaining three numsystems.

Describe the format and use of binary-coded decimal (BCD) numbers.

Determine the ASCII code for any alphanumeric data by using the ASCII ctranslation table.


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Digital versus Analog

Digital systems operate on discrete digits that represent numbers, lette

symbols.

They deal strictly with ON and OFF states, which we can represent by


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Digital versus Analog

Analog systems measure and respond to continuously varying electrica

physical magnitudes.

Analog devices are integrated electronically into systems to continuous

monitor and control such quantities as temperature,pressure,velocit

position and to provide automated control based on the levels of thesquantities.


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Digital vs Analog


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Analog to Digital Conversion


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Digital to Analog Conversion


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Unwanted Noise vs Analog vs Digit


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Advantages of Digital over Analog

Advantage Disadvantage

1. Noise immunity 1. Almost all signals around you is in ana

2. Easy to save and retrieve information

3. Cheaper than Analog counterpart

4. Error corrections and detections techniques5. Uses less bandwidth

6. More flexible than analog


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Review Questions

1. Complete the following sentences with the word analog or digital:a) Wind speed is an example of a(an) _______ quantity?b) A music CD contains _______ information?c) A USB connector transmits _______ data?d) Hourly outdoor air temperatures exhibit _______ variations?

2. An automobile speedometer display is (digital, analog, or could beeither)

3. An analog-to-digital converter outputs an analog voltage. True orfalse?

4. A music CD player is an example of a(n) (ADC or DAC) process?


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Numbering System

Decimal Numbering System (Base 10)

In the decimal numbering system, each position contains 10 different p

digits.

These digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each position in a multi-diwill have a weighting factor based on a power of 10.


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Number Systems

Binary Numbering System (Base 2)

Digital electronics use the binary numbering system because it uses

digits 0 and 1, which can be represented simply in a digital system by

distinct voltage levels, such as +5 V = 1 and 0 V = 0.


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Number Systems

Octal Numbering System (Base 8)The octal numbering system is a method of grouping binary numbersin groups of three.

The eight allowable digits are 0, 1, 2, 3, 4, 5, 6, and 7.

The octal numbering system is used by manufacturers of computers

that utilize 3-bit codes to indicate instructions or operations to beperformed.

By using the octal representation instead of binary, the user can simplifythe task of entering or reading computer instructions and thus savetime.


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Number Systems

Hexadecimal Numbering System (Base 16)

The hexadecimal numbering system, like the octal

system, is a method of grouping bits to simplify

entering and reading the instructions or data present in

digital computer systems.


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Number Systems

Binary-Coded-Decimal SystemThe binary-coded-decimal (BCD) system is used torepresent each of the 10 decimal digits as a 4-bit binarycode. This code is useful for outputting to displays that arealways numeric (0 to 9), such as those found in digital

clocks or digital voltmeters.

To form a BCD number, simply convert each decimal digitto its 4-bit binarycode.


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Summary of

Number Systems


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Coding Scheme

The ASCII CodeMost industry has settled on aninput/output (I/O) code called theAmerican Standard Code forInformation Interchange (ASCII). The

ASCII code uses 7 bits to represent allthe alphanumeric data used incomputer I/O. Seven bits will yield 128different code combinations.


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Documents

CHAPTER 1 - Number Systems, Codes and Applications