1.4 + 1.5

Representing textRepresenting text

• Each of different symbol on the text (alphabet letter) is assigned a unique bit patterns

• the text is then representing as a long string of bits.– ASCII” American standard code for information interchange”:

Uses patterns of 7-bits to represent most symbols used in written English text.

– Today, it is extended to 8-bits.

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Figure 1.13 The message “Hello.” in Figure 1.13 The message “Hello.” in ASCIIASCII

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Representing Text:

• The American National Standards Institute (ANSI) adapted the American Standard Code for Information Interchange (ASCII)

• This code uses 7 bits to represent the alphabets (a-z

& A-Z) and numbers from 0 to 9 and punctuation symbols.

Unicode:

• This code uses 16 bits represents each symbols.

• Unicode consists of 65536 different bit patterns enough to allow text written in such languages

• A file containing a long sequence of symbols encoded using ASCII or Unicode is often called a text file

Representing textRepresenting text

• Unicode: Uses patterns of 16-bits to represent the major symbols used in languages world side

• ISO standard: Uses patterns of 32-bits to represent most symbols used in languages world wide

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The difference between word processors and text file as follows:

Text file Word processors

1Use text editor Use word application

2Contains only character-by-

character encoding of text

Contains numbers proprietary codes representing changes in fonts, alignment information, …etc

3Use ASCII or Unicode Use proprietary code rather than the ASCII or Unicode

Representing Numeric ValuesRepresenting Numeric Values

• Binary notation is a way of representing numeric values using only digits 0 and 1.

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Representing Numeric ValuesRepresenting Numeric Values

• A number can be represented differently in different systems. For example, the two numbers (2A)16 and (52)8 both refer to the same quantity, (42)10, but their representations are different.

• Each number system is associated with a base

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Representing Numeric ValuesRepresenting Numeric Values

• A number represented as:

• Each digit carries a certain weight based on its position

Integer Fraction

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Binary systemBinary system

• In the binary system, there are only two symbols or possible digit values, 0 and 1. This base-2 system can be used to represent any quantity that can be represented in decimal or other number system

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Binary systemBinary system

• For example, here is (11001)11001)22 in binary

• (101.11)(101.11)22

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DecimalDecimal

• The decimal system is composed of 10 numerals or symbols. These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9; using these symbols as digits of a number, we can express any quantity.

• The decimal system, also called the base-10 system

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Decimal systemDecimal system

• (224)(224)1010

• Note that the digit 2 in position 1 has the value Note that the digit 2 in position 1 has the value 20, but the same digit in position 2 has the 20, but the same digit in position 2 has the value 200value 200

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Figure 1.15 The base ten and binary Figure 1.15 The base ten and binary systemssystems

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Figure 1.16 Decoding the binary representation Figure 1.16 Decoding the binary representation 100101100101

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ExerciseExercise

• Convert each of the following binary representation to its base ten:–0101–1001–1011–0110–1000–10010

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Figure 1.17 An algorithm for finding the Figure 1.17 An algorithm for finding the binary representation of a positive integerbinary representation of a positive integer

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Figure 1.18 Applying the algorithm in Figure 1.18 Applying the algorithm in Figure 1.15 to obtain the binary Figure 1.15 to obtain the binary

representation of thirteenrepresentation of thirteen

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Binary additionBinary addition

• To add two integers represented in binary notation, we follow the same procedure in the traditional base ten except that all sums are computed using the following addition fact.

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Binary additionBinary addition

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Binary additionBinary addition

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Binary additionBinary addition

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Fraction in binaryFraction in binary

• The digit to the right of radix point represent the fractional part.

• The positions are assigned fractional quantities

• The first position is assigned the quantity ½ (which is 2-1), and so on

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Fraction in binaryFraction in binary

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Decimal fraction to binaryDecimal fraction to binary

• Covert 0.625 to base 2625 x 2 = 1.25

.625 = .1

25 x 2 = 0.50

.625 = .10

.50 x 2 = 1.00

.625 = .101

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