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COMPUTER SCIENCE Data Representation and Machine Concepts Section 1.5 Instructor: Lin Chen Sept...
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COMPUTER SCIENCE Data Representation and Machine Concepts Section 1.5 Instructor: Lin Chen Sept 2013
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Binary Notation 1 Data Storage Recall How to convert binary notation to decimal notation How to convert decimal notation to binary notation Convert to decimal notation Convert to binary notation
Transcript of COMPUTER SCIENCE Data Representation and Machine Concepts Section 1.5 Instructor: Lin Chen Sept...
COMPUTER SCIENCEData Representation and Machine ConceptsSection 1.5
Instructor: Lin ChenSept 2013
1.5 The Binary System
1 Data Storage
Binary Notation
Binary Addition
Fractions in Binary
Pearson Custom: Computer Science, Data Representation and Machine Concepts
Binary Notation
1 Data Storage
RecallHow to convert binary notation to decimal notationHow to convert decimal notation to binary notation
Convert 11010012 to decimal notation
Convert 12310 to binary notation
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
0
1
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
10
11
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
110
11
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
1110
11
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
01110
111
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
001110
1111
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
1001110
1111
Binary Addition
1 Data Storage
Binary addition rule
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 101 + 1 + 1 = 11
10010011+ 111011
11001110
1111
Binary Addition
1 Data Storage
1001001+ 0011001
1000111+ 0010110
Questions:
http://www.atilim.edu.tr/~compe111/
Fractions in Binary
1 Data Storage
Convert fractional binary number to decimal number
1 0 . 0 1 1 = 1* 21 + 0*20 + 0*2-1 + 1*2-2 + 1*2-3
= 2 + 0 + 0 + + = 2.375
1 0 -1 -2 -3
Questions:Convert following two base notations to their equivalent ten base notation
100.110 111.001 0.101
Fractions in Binary
1 Data Storage
Convert fractional decimal number to binary number
2.375
Integer Part Fractional Part
210 = 102 0.375 * 2 = 0.75 0
0.75 * 2 = 1.5 1
0.5 * 2 = 1.0 1
10.011
Fractions in Binary
1 Data Storage
Questions:Convert following fractional decimal number to binary number
4.5 1.125 10.1
Fractions in Binary
1 Data Storage
Addition
10.011+ 100.110
1. Align radix point2. Do addition with the binary addition rule
