business programming i fall – 2000 by jim payne lecture 04jim payne - university of tulsa2 storage...

Business Programming I

Fall – 2000By

Jim Payne

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Storage and Data

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What do we store?

Numbers 0,1,2,3, etc. Alphabetic Characters A,B,C, a,b,c Special Symbols * ( [ { ? / + : Pictures Sounds Motion Pictures

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Numbering Systems

Decimal Numbering System Hexadecimal Numbering System Octal Numbering System Binary Numbering System

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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?

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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

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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

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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

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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

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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

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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

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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.

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Octal Numbering System

Uses 8 unique characters 0 1 2 3 4 5 6 7

We are not familiar with it

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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

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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

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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.

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Binary Numbering System

Uses 2 unique characters 0 1

We WILL become much more familiar with it

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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

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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

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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.

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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

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2 3 2 2 2 1 2 0

8 4 2 1

Let’s learn to count in binary…

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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

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What is the Binary Equivalent of: 8 4 2 1

11 13 7 4 6 3 15

1011 1101 111 100 110 11 1111

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