chapter 3 representing numbers and text in binary
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Chapter 3 Representing Numbers and Text in Binary. Information Technology in Theory By Pelin Aksoy and Laura DeNardis. Binary Coded Decimal. Binary coded decimal (BCD) is a different approach Encodes each digit in the decimal number individually rather than converting the entire number - PowerPoint PPT PresentationTRANSCRIPT
Chapter 3Representing Numbers and
Text in Binary
Information Technology in Theory
By Pelin Aksoy and Laura DeNardis
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Binary Coded Decimal
• Binary coded decimal (BCD) is a different approach
• Encodes each digit in the decimal number individually rather than converting the entire number
• To convert 30 to BCD, the 3 would first be converted into binary, and then 0 would be converted into binary
• Then the two binary strings would be concatenated (i.e. brought together) to represent the number 30
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Binary Coded Decimal (continued)
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BCD Example
Convert the decimal number 7244(10) into binary coded decimal
7 = 01112 = 00104 = 01004 = 0100
7244(10) = 0111001001000100(2) (BCD)
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BCD Example (continued)
Convert the sequence 0001100001111001 into decimal
First break the sequence into groups of four starting from right to left: 0001 1000 0111 1001
Then convert each group into decimal:0001(2) = 1(10)
1000(2) = 8(10)
0111(2) = 7(10)
1001(2) = 9(10)
The answer is 1879(10)
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Representing Text and Other Characters in Binary
• Binary code can represent text and alphanumeric characters
• Two standards: – ASCII – Unicode
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ASCII• Extended ASCII assigns an 8-bit code for each
alphanumeric character • Recall that an 8-bit code can represent 28, or 256,
unique items
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Segment of ASCII Chart
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ASCII Example
H = 01001000e = 01100101l = 01101100l = 01101100o = 01101111! = 100100001
Therefore, “Hello!” = 0100100001100101011011000110110001101111. The hexadecimal shorthand for this binary sequence is 48 65 6C 6C 6F 21
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Unicode
• Unicode is an important standard that uses 16 bits• Allows for a representation of 216 (more than
65,000) unique characters • Provides sufficient characters to encode many
different major languages (such as English, Arabic, and Chinese)
• Unicode charts may be found by visiting http://unicode.org
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EBCDIC
• Extended Binary Coded Decimal Interchange Code
• Standard associated with IBM computers
• Assigns 8 bits per character
• An extension of binary coded decimal
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Summary
• Bits can encode any type of information, including the decimal numbers we use in everyday life and alphanumeric text
• A real-world example of binary to decimal conversion is the unique Internet address– Encoded in dotted decimal format – Makes a long binary string easier for people to
read• You can also convert between binary and positive
integers and represent negative integer and positive noninteger numbers in binary
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Summary (continued)
• Alternative numbering systems are octal, which uses eight numbers, and hexadecimal, which uses 16 numbers– Not used by digital devices, but by people as a
shorthand convention – Network identification in local area networks is
usually represented in hexadecimal • Binary code also represents alphanumeric
characters – ASCII– Unicode– EBCDIC
Information Technology in Theory