business programming i fall – 2000 by jim payne lecture 04jim payne - university of tulsa2 storage...
TRANSCRIPT
Business Programming I
Fall – 2000By
Jim Payne
2Jim Payne - University of TulsaLecture 04
Storage and Data
3Jim Payne - University of TulsaLecture 04
What do we store?
Numbers 0,1,2,3, etc. Alphabetic Characters A,B,C, a,b,c Special Symbols * ( [ { ? / + : Pictures Sounds Motion Pictures
4Jim Payne - University of TulsaLecture 04
Numbering Systems
Decimal Numbering System Hexadecimal Numbering System Octal Numbering System Binary Numbering System
5Jim Payne - University of TulsaLecture 04
Decimal Numbering System
Uses 10 unique characters 0 1 2 3 4 5 6 7 8 9
We are very familiar with it
For example:
Is 1325 a large number? What does 1325 mean?
6Jim Payne - University of TulsaLecture 04
Here is what it means:
If we built a number line for a decimal number, it would look like this:
10 4 10 3 10 2 10 1 10 0
10000 1000 100 10 1
1 3 2 5
7Jim Payne - University of TulsaLecture 04
Let’s assume we did not know this.
10 4 10 3 10 2 10 1 10 0
10000 1000 100 10 1
1325/base 10 = 132 R 5 132/10 = 13 R 2
13/10 = 1 R 3 1/10 = 0 R 1
1 3 2 5
8Jim Payne - University of TulsaLecture 04
To Check Our Answer:
110100100010000
10 010 110 210 310 4
1 3 2 5
1*1000 = 1000
3*100 = 300
2*10 = 20
5*1 = 5
------------------
Sum = 1325
9Jim Payne - University of TulsaLecture 04
Hexadecimal Numbering System
Uses 16 unique characters 0 1 2 3 4 5 6 7 8 9 A B C D E
F
We are not familiar with it
10Jim Payne - University of TulsaLecture 04
Hexadecimal – 0 1 2 3 4 5 6 7 8 9 A B
C D E F
16 4 16 3 16 2 16 1 16 0
65536 4096 256 16 1
1325/16 = 82 R D 82/16 = 5 R 2
5/16 = 0 R 5
5 D 2
11Jim Payne - University of TulsaLecture 04
To Check Our Answer:
116256409665536
16 016 116 216 316 4
5 2 D
5*256 = 1280
2*16 = 32
D*1 = 13
------------------
Sum = 1325
Lecture 04 Jim Payne - University of Tulsa 12
What have we learned?
We just learned that 52D is the hexadecimal equivalent of the decimal number 1325.
If 1325 is a large number of gold bars or a small amount of sand, then so is 52D to someone that grew up in the hexadecimal numbering system.
13Jim Payne - University of TulsaLecture 04
Octal Numbering System
Uses 8 unique characters 0 1 2 3 4 5 6 7
We are not familiar with it
14Jim Payne - University of TulsaLecture 04
Octal – 0 1 2 3 4 5 6 7
8 4 8 3 82 8 1 8 0
4096 512 64 8 1
1325/8 = 165 R 5 165/8 = 20 R 5
20/8 = 2 R 4 2/8 = 0 R 2
2 4 5 5
15Jim Payne - University of TulsaLecture 04
To Check Our Answer:
18645124096
8 0818 28 38 4
2 4 5 5
2*512 = 1024
4*64 = 256
5*8 = 40
5*1 = 5
------------------
Sum = 1325
Lecture 04 Jim Payne - University of Tulsa 16
What have we learned?
We have just learned, that 2455 is the octal equivalent of the hexadecimal 52D, which of course is the decimal equivalent of 1325.
They are all the same NUMBER, just different numbering systems.
17Jim Payne - University of TulsaLecture 04
Binary Numbering System
Uses 2 unique characters 0 1
We WILL become much more familiar with it
18Jim Payne - University of TulsaLecture 04
Binary - 0 1
1325/2 = 662 R 1 662/2 = 331 R 0 331/2 = 165 R 1
165/2 = 82 R 1
210 29 28 27 26 25 24 23 22 21 20
1024
512 256
128
64 32 16 8 4 2 1
82/2 = 41 R 0 41/2 = 20 R 1
20/2 = 10 R 0 10/2 = 5 R 0 5/2 = 2 R 1
2/2 = 1 R 0 1/2 = 0 R 1
101 1
0 10 0 1
0 1
19Jim Payne - University of TulsaLecture 04
To Check Our Answer:
210 29 28 27 26 25 24 23 22 21 20
1024
512 256 128 64 32 16 8 4 2 1
1 0 1 0 0 1 0 1 1 0 1
Notice – No Multiplication:
1024 + 256 + 32 + 8 + 4 + 1 = 1325
Lecture 04 Jim Payne - University of Tulsa 20
So,…. obviously,…
10100101101 is the binary equivalent of the octal 2455, the hexadecimal 52D, and the decimal 1325.
You might not find the repetitive division process exciting, but you could all do it if you had to…
So, obviously, any one of you could take any decimal number and convert it into it’s binary equivalent by a process of division by 2….
It turns out, that division by 2 is something a computer chip can do very very fast.
21Jim Payne - University of TulsaLecture 04
Let’s try a few new numbers:
210 29 28 27 26 25 24 23 22 21 20
1024
512 256 128 64 32 16 8 4 2 1
22Jim Payne - University of TulsaLecture 04
2 3 2 2 2 1 2 0
8 4 2 1
Let’s learn to count in binary…
23Jim Payne - University of TulsaLecture 04
2 3 2 2 2 1 2 0
8 4 2 1
1
1 0
1 1
1 0 0
1 0 1
1 1 0
1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
Lecture 04 Jim Payne - University of Tulsa 24
What is the Binary Equivalent of: 8 4 2 1
11 13 7 4 6 3 15
1011 1101 111 100 110 11 1111
25Jim Payne - University of TulsaLecture 04