Number Systems. Lesson 1

1. 1. Number Systems

ITEC 1011
Introduction to Information Technologies

2. Common Number Systems

Used by
humans?
Used in
computers?
System
Base Symbols
Decimal
10
0, 1, … 9
Yes
No
Binary
2
0, 1
No
Yes
Octal
8
0, 1, … 7
No
No
Hexadecimal
16
0, 1, … 9,
A, B, … F
No
No
ITEC 1011
Introduction to Information Technologies

3. Quantities/Counting (1 of 3)

Decimal
0
1
2
3
Binary
0
1
10
11
HexaOctal decimal
0
0
1
1
2
2
3
3
4
5
6
100
101
110
4
5
6
4
5
6
7
111
7
7
p. 33
ITEC 1011
Introduction to Information Technologies

4. Quantities/Counting (2 of 3)

ITEC 1011
HexaOctal decimal
10
8
11
9
12
A
13
B
Decimal
8
9
10
11
Binary
1000
1001
1010
1011
12
13
14
1100
1101
1110
14
15
16
C
D
E
15
1111
17
F
Introduction to Information Technologies

5. Quantities/Counting (3 of 3)

ITEC 1011
Decimal
16
17
18
19
Binary
10000
10001
10010
10011
HexaOctal decimal
20
10
21
11
22
12
23
13
20
21
22
10100
10101
10110
24
25
26
14
15
16
23
10111
27
17
Introduction to Information Technologies
Etc.

6. Conversion Among Bases

• The possibilities:
Decimal
Octal
Binary
Hexadecimal
pp. 40-46
ITEC 1011
Introduction to Information Technologies

7.

Weight
12510 =>
5 x 100
2 x 101
1 x 102
=
5
= 20
= 100
125
Base
ITEC 1011
Introduction to Information Technologies

8. Example

Bit “0”
1010112 =>
1 x 20 =
1 x 21 =
0 x 22 =
1 x 23 =
0 x 24 =
1 x 25 =
1
2
0
8
0
32
4310
ITEC 1011
Introduction to Information Technologies

9. Example

7248 =>
ITEC 1011
4 x 80 =
2 x 81 =
7 x 82 =
4
16
448
46810
Introduction to Information Technologies

10. Example

ABC16 =>
C x 160 = 12 x
1 =
12
B x 161 = 11 x 16 = 176
A x 162 = 10 x 256 = 2560
274810
ITEC 1011
Introduction to Information Technologies

11. Exercise – Convert ...

Decimal
33
Binary
Octal
Hexadecimal
1110101
703
1AF
Don’t use a calculator!
Skip answer
ITEC 1011
Introduction to Information Technologies
Answer

12. Exercise – Convert …

Answer
ITEC 1011
Hexadecimal
Decimal
33
Binary
100001
Octal
41
117
1110101
165
75
451
111000011
703
1C3
431
110101111
657
1AF
Introduction to Information Technologies
21