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Binary numbers


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#1
Will_00

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Here is an explanation of Binary:

As you may know, instead of using all of the natural numbers, binary uses only 0 and 1's. As quoted by Wikipedia "When the symbols for the first digit are exhausted, the next-higher digit (to the left) is incremented," and then is released to the next 0. Example:

In decimal system numbers run as thus:

001, 002, 003, 004 (As the number on the far right ends it precedes to the next number)
008, 009, 010 (And therefor as the numbers increase it addes a 0 to the end)

In binary it follows as thus:

000, 001, 010, 011 (In binary it runs with virtually the same effect, except it uses only 0's and 1's.)
So the next one would be 100, 101, etc.

Here is the relation between the hexadecimal system:

Hex Dec Binary
0 0 0000
1 1 0001
2 2 0010
3 3 0011

Hex Dec Binary
4 4 0100
5 5 0101
6 6 0110
7 7 0111

Hex Dec Binary
8 8 1000
9 9 1001
A 10 1010
B 11 1011

Hex Dec Binary
C 12 1100
D 13 1101
E 14 1110
F 15 1111

To convert a hexadecimal number to it's decimal equivalent - according to wikipedia - "multiply the decimal equivalent of each hexadecimal digit by the corresponding power of 16 and add the resulting values:"

C0E716 = (12 × 163) + (0 × 162) + (14 × 161) + (7 × 160) = (12 × 4096) + (0 × 256) + (14 × 16) + (7 × 1) = 49,38310


Whilst converting to the octal system it would follow as thus:

Octal Binary
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111


This is due because octal uses a radix of 8.

Anything else to add?
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#2
Chopin

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Yeah. Ask if you can get it pinned in the GeekU underclass library.
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#3
ScHwErV

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Why on earth would this be something we would need in GeekU? We do very little with Binary.
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#4
sari

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To be honest, I'm not sure of the point of this at all. The vast majority of people have no need for this information, and those that might need it (I learned all this in my college programming courses, for example) have probably already been exposed to it. For anyone that might be interested, this information is readily available through a quick search (and probably without the spelling errors).
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#5
Chopin

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:) Sure, why not :)

Edited by Fredil Yupigo, 25 February 2008 - 05:00 PM.

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