9781423901402_PPT_Ch03 - Information Technology in Theory...

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Chapter 3 Representing Numbers and Text in Binary Information Technology in Theory By Pelin Aksoy and Laura DeNardis
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2 Objectives Understand the binary numbering system Mathematically convert numbers between decimal and binary Understand binary coded decimal (BCD) representation Information Technology in Theory
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3 Objectives (continued) Learn about alternative numbering systems such as octal and hexadecimal and explain their significance in information technology Provide real-world examples of binary and hexadecimal representation in information technology Convert alphanumeric text into binary Information Technology in Theory
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4 The Binary Numbering System Any information can be represented in binary Binary is a code with two symbols, 0 and 1 To understand binary, it’s helpful to think about how the decimal system works Information Technology in Theory
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5 Think About the Decimal System Information Technology in Theory
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6 The Base 10 System Decimal digits are combined to create larger numbers 4268.25 = (4 x 10 3 ) + (2 x 10 2 ) + (6 x 10 1 ) + (8 x 10 0 ) + (2 x 10 –1 ) + (5 x 10 –2 ) 10 raised to the power of. .. 10 –2 =1/(10x10)=0.01 10 –1 =1/10=0.1 10 0 =1 10 1 =10 10 2 =10x10=100 10 3 =10x10x10=1000 10 4 =10x10x10x10=10,000 and so on. .. Therefore, decimal is also called the base 10 system Information Technology in Theory
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7 Base-2 System Binary is referred to as the base-2 system How do we count above 1? As in the decimal system, each placeholder has its own weighting The weightings are based on powers of 2 instead of powers of 10 The last digit has a value of 1 and occupies the “8s place” Information Technology in Theory
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8 Base-2 System (continued) The number 1010 is made up of four digits The rightmost 0 occupies the “1s place” The next digit has a value of 1 and occupies the “2s place” The next digit has a value of 0 and occupies the “4s place” The last digit has a value of 1 and occupies the “8s place” Information Technology in Theory
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9 Binary to Decimal Integer Conversion 1011.11 = (1 x 2 3 ) + (0 x 2 2 ) + (1 x 2 1 ) + (1 x 2 0 ) + (1 x 2 1 ) + (1 x 2 –2 ) 2 raised to the power of. .. 2 –4 =1/(2x2x2x2)=0.0625 2 –3 =1/(2x2x2)=0.125 2 –2 =1/(2x2)=0.25 2 –1 =1/2=0.5 2 0 =1 2 1 =2 2 2 =2x2=4 2 3 =2x2x2=8 and so on. ... Information Technology in Theory
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10 Binary to Decimal Integer Conversion Information Technology in Theory
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11 Converting an 8-bit Number into Decimal Information Technology in Theory
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12 Real-World Example of Binary to Decimal Conversion Every computing device connecting to the Internet uses a unique identifier, known as an IP (Internet Protocol) address Addresses are either 32 or 128 bits long An example of an address is: 01000111001111001001100010100000 Dotted decimal format condenses the addresses For example 71.60.152.160 Information Technology in Theory
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13 Converting to Dotted Decimal Format Step 1: Break the binary address into four groups of 8 bits Step 2: Convert each group of 8 bits into decimal Step 3: Separate each of the four resulting numbers with dots Information Technology in Theory
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14 Example
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9781423901402_PPT_Ch03 - Information Technology in Theory...

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