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