1. Lecturer: Santokh Singh
CompSci 105 SS 2005
Principles of Computer Science
Lecture 2
Lecturer: Santokh Singh

2. Numbers in the Computer
Binary representation of integers
Octal representation of integers
Hexadecimal representation of integers
Binary Arithmetic
Addition
Subtraction
Using Bits as Bits
Logical Operations

3. Positive Integers
In the range 0-3 …. 11 00 01 10

4. Decimal Numbers 2 1 7 3

5. Decimal Numbers
1000
100 10 1 2 1 7 3

6. Decimal Numbers
103
102
101
100 2 1 7 3

7. Binary Numbers 1 1 1

8. Binary Numbers 23 22 21 20 1 1 1

9. Binary Numbers 8 4 2 1 1 1 1

10. Exercise
Convert the binary number to decimal

11. Converting to Binary
1011 11 ?
1011 11

12. Digit Manipulation
Removing the last digit of a number
Extracting the last digit of a number
2173
217 ?
2173 3 ?

13. Extract in Right to Left Order
2173

14. Converting to Binary Repeat until number is empty
Extract last binary digit
Remove last binary digit

15. Exercise
Convert the decimal number 77 to binary

16. Numbers in the Computer
Binary representation of integers
Octal representation of integers
Hexadecimal representation of integers
Binary Arithmetic
Addition
Subtraction
Using Bits as Bits
Logical Operations

17. 1 5 + 6 1 2 + 3 8 7 + 15 1 + 2 6 4 + 10 2 3 + 5 9 + 18 3 7 + 10 1 +

18. 1 1 + + 1 + + 1 1 1 10

19. 1 1 1 + 1 1 1

20. 1 1 1 - 1 1

21. Exercises
Perform the following binary calculations. Convert to base 10 to check your answer:
101110
101110

22. If binary is so much easier, why do we use base 10 for most things?

23. If binary is so much easier, why do we use base 10 for most things?
275

24. Numbers in the Computer
Binary representation of integers
Octal representation of integers
Hexadecimal representation of integers
Binary Arithmetic
Addition
Subtraction
Using Bits as Bits
Logical Operations

25. Octal 1 2 3
000
001
010
011 4 5 6 7
100
101
110
111

28. Hexadecimal
0001 1
0010 2
0000
0011 3
0101 5
0110 6
0100 4
0111 7
1001 9
1010 A
1000 8
1011 B
1101 D
1110 E
1100 C
1111 F

29. Hex Numbers and Bytes
1000
1011
0010
0011

30. Course Book Notes for 1st and 2nd lecture:-
Pages : Numbers in the Computer
Pages : Data Representations