Numbering Systems:
As you know, computers use a BINARY
numbering system ( 0, 1 ). Every key that you enter is converted into a series
of zeros and ones.
The letter H = 00010011
- The letter E = 00101101 The number
5 = 00110101
* See ASCI chart
Decimal = Base 10 ( the one we know and
love )
Octal = Base 8
Binary = Base 2
Hexadecimal = A "shortcut"
method of representing binary numbers.
Lets start with converting Base 10
numbers to base 2 (Binary)
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1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
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32768 |
16384 |
8192 |
4096 |
2048 |
1024 |
512 |
256 |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
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Value |
= |
11 |
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0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
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Value |
= |
32 |
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0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
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Value |
= |
31 |
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0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
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Value |
= |
129 |
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1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
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Value |
= |
1 |
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0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
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HEXadecimal is used as an efficient way to store many binary numbers.
It takes binary numbers and breaks them into four digit groups. It then uses the numbers 0-9 and A-F
A=10, B=11, C=12, D=13, E=14, F=15
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B=30 |
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0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
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HEX=1F |
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1 |
F |
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B= 283 |
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1 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
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HEX=F3 |
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F |
3 |
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The OCTAL system does
the same thing using 3 digit groups instead of 4.
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B=30 |
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0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
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Octal=036 |
0 |
3 |
6 |
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B= 283 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
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Octal=363 |
3 |
6 |
3 |
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