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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 ten12345 =
5 * 1 +
4 * 10 +
3 * 100 +
2 * 1000 +
1 * 10,000
Binary Numbers
• Each Digit is a power of two10110 =
1 * 0 +
2 * 1 +
4 * 1 +
8 * 0 +
16 * 1
= 22
Binary Numbers
• Each Digit is a power of two1011101 =
= 93
1 * 1 +
2 * 0 +
4 * 1 +
8 * 1 +
16 * 1+
32 * 0 +
64 * 1
Why Binary?
• Any physical phenomenon that has two states can be used to store a binary number
11010 = 26
Magnetism
+ - + - + +
MagneticMaterial
Read/Write Head1
101011 = 43
Voltage
+5 +5 +50 0 0
100101 = 37
Holes in PaperLight = 1Dark = 0
101010 = 42
PhotoSensor
Light
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 numbersIntegers 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 PointBooleans (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 false6!=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 65B 66C 67D 68E 69F 70G 71H 72I 73J 74K 75. . .Z 90
What is special about the order of the numbers?
a 97b 98c 99d 100e 101f 102g 103h 104I 105j 106k 107. . .z 122
Type ‘g’Store 103
ASCII Code for Characters
A 65B 66C 67D 68E 69F 70G 71H 72I 73J 74K 75. . .Z 90
A numeric character is different from its ASCII number
a 97b 98c 99d 100e 101f 102g 103h 104I 105j 106k 107. . .z 122
0 481 492 503 514 525 536 547 558 569 57
ASCII Code for Characters
A 65B 66C 67D 68E 69F 70G 71H 72I 73J 74K 75. . .Z 90
Dad32@Abc
a 97b 98c 99d 100e 101f 102g 103h 104i 105j 106k 107. . .z 122
0 481 492 503 514 525 536 547 558 569 57
. 46- 45+ 43@ 64$ 36% 37& 38 space 32* 42( 40) 41
68 97 100 51 50 64 65 98 99
What about Chinese, Sanscrit, Hebrew, Cyrillic, etc ??A 65B 66C 67D 68E 69F 70G 71H 72I 73J 74K 75. . .Z 90
a 97b 98c 99d 100e 101f 102g 103h 104I 105j 106k 107. . .z 122
0 481 492 503 514 525 536 547 558 569 57
. 46- 45+ 43@ 64$ 36% 37& 38 space 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 65B 66C 67D 68E 69F 70G 71H 72I 73J 74K 75. . .Z 90
a 97b 98c 99d 100e 101f 102g 103h 104I 105j 106k 107. . .z 122
0 481 492 503 514 525 536 547 558 569 57
. 46- 45+ 43@ 64$ 36% 37& 38 space 32* 42( 40) 41
‘A’ + 2 = ‘C’‘g’- ‘d’ = 3‘F’ + 32 = ‘f’
‘A’ < ‘D’ is true‘%’ >= ‘+’ is false
Information
• Binary numbers
• Integers and Floating Point
• Booleans (True, False)
• CharactersVariables
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 75B ?C ?
Program
• A sequence of things to do
A = 75;
B = A+13;
A = A-B+3;
C = A/2 + 1;
A 75B 88C ?
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 -10B 88C ?
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 -10B 88C -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
