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

17. ONE’S COMPLEMENT
17

18. 2’s 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/