Applied physics iii lecture2 number_systemsii
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This document discusses number systems and arithmetic operations in applied physics III. It covers addition and subtraction of binary, hexadecimal, and octal numbers. It also discusses representing negative numbers in computers by using the most significant bit as the sign bit, with 0 indicating positive and 1 indicating negative. Examples of ones' complement and twos' complement representation of negative numbers are provided. References for further reading on number systems and arithmetic are listed at the end.
Applied physics iii lecture2 number_systemsii
- 1. Applied physics III Number systems: Arithmetic Operations 1 by Benson Mbuya
- 2. Review of basic concepts of arithmetic 2
- 3. Addition and subtraction of binary numbers 3
- 4. Add the binary numbers 01010 and 10111 4
- 5. Subtract 111 from 10001 5
- 6. Hexadecimal Addition & Subtraction Hexadecimal Addition Carry generated Hexadecimal Subtraction Borrow weight 16
- 7. Hexadecimal Addition Carry 1 + 2AC6 92B5 BD7B 6+5=11d Bh C+B=23d 17h A+2+1=13d Dh 2+9=11d Bh
- 8. Hexadecimal Subtraction Borrow - 111 92B5 2AC6 67EF 21-6=15d Fh 26-C=14d Eh 17-A=7d 7h 8-2=6d 6h
- 9. Octal Addition & Subtraction Octal Addition Carry generated Octal Subtraction Borrow weight 8
- 10. Octal Addition Carry 1 + 7602 5771 15573 2+1=3d 3O 0+7=7d 7O 6+7=13d 15O 1+7+5=13d 15O
- 11. Octal Subtraction Borrow - 11 7602 5771 1611 2-1=1d 1O 8-7=1d 1O 13-7=6d 6O 6-5=1d 1O
- 12. Addition and subtraction of hexadecimal numbers 12
- 13. 13
- 14. 14
- 15. Representing negative numbers in a computer By convention the leftmost bit (or most significant bit) is considered the sign bit. A value of 0 in the sign bit indicates a positive number, whereas a 1 indicates a negative number. 15
- 16. examples 16
- 18. 2s Complement 18
- 19. references Chapter 30, Teach yourself electronics, 3rd ed, Stan Gibilisco. Chapter 4, digital electronics demystified, Myke Predko. Chapter 18, Schaums outline: basic mathematics with applications to science and technology, Kruglak, Moore. http://www.electronics.dit.ie/staff/tscarff/number_syste ms/number_systems.html http://active.tutsplus.com/tutorials/codingconcepts/number-systems-an-introduction-to-binaryhexadecimal-and-more/ http://www.math.grin.edu/~rebelsky/Courses/152/97F/ Readings/student-binary http://active.tutsplus.com/tutorials/codingconcepts/number-systems-an-introduction-to-binary19 hexadecimal-and-more/