Download CS%20100-02-NumbersAndChars

Information and Programs
Foundations of Computing
• Information
–
–
–
–
–
Binary numbers
Integers and Floating Point
Booleans (True, False)
Characters
Variables
• Programs
– Expressions
– Assignment
– Sequences
Information
Binary numbers
• Integers and Floating Point
• Booleans (True, False)
• Characters
• Variables
Decimal Numbers
• Each digit is a power of ten
12345 =
5*1+
4 * 10 +
3 * 100 +
2 * 1000 +
1 * 10,000
Binary Numbers
• Each Digit is a power of two
10110 =
1*0+
2*1+
4*1+
8*0+
16 * 1
= 22
Binary Numbers
• Each Digit is a power of two
1011101 =
1*1+
2*0+
4*1+
8*1+
16 * 1+
32 * 0 +
64 * 1
= 93
Why Binary?
• Any physical phenomenon that has two
states can be used to store a binary number
11010
= 26
Magnetism
Magnetic
Material
Read/Write Head
1
+-+-++
101011
= 43
Voltage
+5 0
0
+5 0 +5
100101
= 37
Holes in Paper
Light = 1
Dark = 0
Photo
Sensor
Light
101010
= 42
Binary Students
• Male = 0
• Female = 1
Why Binary?
• Any physical phenomenon that has two
states can be used to store a binary number
• Each binary digit is called a BIT
– 1010 - is a 4 bit number
– 01010100 - is an 8 bit number
• An 8 bit number is called a BYTE
Size of a Binary
Number
• How many different numbers can you store in 2
bits?
• How many can you store in 8 bits?
• In general, 2(number of bits) numbers can be stored
• How many in 10 bits?
– 1024 = 1K
• How many in 20 bits?
– 1,048,576 = 1Meg
Information
• Binary numbers
Integers and Floating Point
• Booleans (True, False)
• Characters
• Variables
Integers
• 100
• 100245
• -45
Size of an Integer
• How many bits required for the number 17?
• 5 bits
• How many bits for the number 1023?
• 10 bits
Integer Expressions
• * means multiply
• / means divide
• 2*4+3 = 11
• 2*(4+3) = 14
• (7+9)/2 = 8
Floating point numbers
• Numbers with decimal points
• 1.23
• 5623.1232
• -0.00232
Floating point numbers
• Numbers with decimal points
• 1.23 = 0.123e1
• 5623.1232 = 0.56231232e4
• -0.00232=-0.232e-2
• Stored differently (sign + fraction + exponent)
Information
• Binary numbers
• Integers and Floating Point
Booleans (True, False)
• Characters
• Variables
Booleans
• 1 = true
• 0 = false
Boolean Expressions
• (7>3) is true
• ((2+4)<6) is false
> Greater than
< less than
<= less than or equal
>= greater than or equal
== equal
!= not equal
7<=6 is false
6!=5 is true
Information
• Binary numbers
• Integers and Floating Point
• Booleans (True, False)
Characters
• Variables
ASCII Code for Characters
• Every character is defined to have an 8 bit
(1 byte) number
A
B
C
D
E
F
G
H
I
J
K
...
Z
65
66
67
68
69
70
71
72
73
74
75
90
a
b
c
d
e
f
g
h
I
j
k
...
z
97
98
99
100
101
102
103
104
105
106
107
Store 103
122
What is special about the order of the numbers?
Type ‘g’
ASCII Code for Characters
A
B
C
D
E
F
G
H
I
J
K
...
Z
65
66
67
68
69
70
71
72
73
74
75
90
a
b
c
d
e
f
g
h
I
j
k
...
z
97
98
99
100
101
102
103
104
105
106
107
0
1
2
3
4
5
6
7
8
9
48
49
50
51
52
53
54
55
56
57
122
A numeric character is different from its ASCII number
ASCII Code for Characters
A
B
C
D
E
F
G
H
I
J
K
...
Z
65
66
67
68
69
70
71
72
73
74
75
90
a
b
c
d
e
f
g
h
i
j
k
...
z
97
98
99
100
101
102
103
104
105
106
107
0
1
2
3
4
5
6
7
8
9
48
49
50
51
52
53
54
55
56
57
.
+
@
$
%
&
space
*
(
)
46
45
43
64
36
37
38
32
42
40
41
122
Dad32@Abc
68 97 100 51 50
64
65 98 99
What about Chinese, Sanscrit,
Hebrew, Cyrillic, etc ??
A
B
C
D
E
F
G
H
I
J
K
...
Z
65
66
67
68
69
70
71
72
73
74
75
90
a
b
c
d
e
f
g
h
I
j
k
...
z
97
98
99
100
101
102
103
104
105
106
107
122
0
1
2
3
4
5
6
7
8
9
48
49
50
51
52
53
54
55
56
57
.
+
@
$
%
&
space
*
(
)
46
45
43
64
36
37
38
32
42
40
41
What about Chinese, Sanscrit,
Hebrew, Cyrillic, etc ??
• UNICODE rather than ASCII
• 2 Bytes per character
– Twice as much space
– 65,536 possible characters
(2^16)
Expressions with characters
A
B
C
D
E
F
G
H
I
J
K
...
Z
‘A’ + 2 = ‘C’
‘g’- ‘d’ = 3
‘F’ + 32 = ‘f’
65
66
67
68
69
70
71
72
73
74
75
90
a
b
c
d
e
f
g
h
I
j
k
...
z
97
98
99
100
101
102
103
104
105
106
107
0
1
2
3
4
5
6
7
8
9
48
49
50
51
52
53
54
55
56
57
.
+
@
$
%
&
space
*
(
)
122
‘A’ < ‘D’ is true
‘%’ >= ‘+’ is false
46
45
43
64
36
37
38
32
42
40
41
Information
• Binary numbers
• Integers and Floating Point
• Booleans (True, False)
• Characters
Variables
Variable
• A named place to store a value
– George = 32
– Size = 17
– Weight = 120
Program
• A sequence of things to do
A = 75;
B = A+13;
A = A-B+3;
C = A/2 + 1;
Program
• A sequence of things to do
A = 75;
B = A+13;
A = A-B+3;
C = A/2 + 1;
A
B
C
75
?
?
Program
• A sequence of things to do
A = 75;
B = A+13;
A = A-B+3;
C = A/2 + 1;
A
B
C
75
88
?
A + 13
75 + 13 = 88
Program
• A sequence of things to do
A = 75;
B = A+13;
A = A-B+3;
C = A/2 + 1;
A
B
C
-10
88
?
A-B+3
75 - 88 + 3 = -10
Program
• A sequence of things to do
A = 75;
B = A+13;
A = A-B+3;
C = A/2 + 1;
A
B
C
-10
88
-4
A/2+1
-10 / 2 + 1 = -4
Review
• Binary numbers (using any two states)
• Integers and Floating Point
– Expressions (+ - * /)
• Booleans (true, false) (< > <= >= == !=)
• Characters
– ASCII, UNICODE
• Variables
• Programs