1. COMPUTER SCIENCE Data Representation and Machine Concepts Section 1.5 Instructor: Lin Chen Sept 2013

2. 1.5 The Binary System 1 Data Storage Binary Notation Binary Addition Fractions in Binary Pearson Custom: Computer Science, Data Representation and Machine Concepts

3. Binary Notation 1 Data Storage Recall How to convert binary notation to decimal notation How to convert decimal notation to binary notation Convert 1101001 2 to decimal notation Convert 123 10 to binary notation

4. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011

5. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011 0 1

6. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011 10 1

7. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011 110 1

8. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011 1110 11

9. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011 01110 111

10. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011 001110 111

11. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011 1001110 111

12. Binary Addition 1 Data Storage Binary addition rule 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 10010011 + 111011 11001110 11

13. Binary Addition 1 Data Storage 1001001 + 0011001 1000111 + 0010110 Questions: http://www.atilim.edu.tr/~compe111/

14. Fractions in Binary 1 Data Storage Convert fractional binary number to decimal number 1 0 -1 -2 -3 Questions: Convert following two base notations to their equivalent ten base notation 100.110111.001 0.101

15. Fractions in Binary 1 Data Storage Convert fractional decimal number to binary number 2.375 Integer PartFractional Part 2 10 = 10 2 0.375 * 2 = 0.75 0 0.75 * 2 = 1.5 1 0.5 * 2 = 1.0 1 10.011

16. Fractions in Binary 1 Data Storage Questions: Convert following fractional decimal number to binary number 4.5 1.125 10.1

17. Fractions in Binary 1 Data Storage Addition 10.011 + 100.110 1.Align radix point 2.Do addition with the binary addition rule