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Re: Binary Sequences Discussion Thread

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ParadigmaticAnon is not online. ParadigmaticAnon
Joined: 25 Jan 2016
Total Posts: 182
12 Feb 2016 10:32 PM
Hello ROBLOX users. The purpose of this thread is to discuss the construction and manipulation of base-two sequences. I will provide an example sequence to facilitate wholesome discussion.

S = 101

This is the decimal equivalent of the binary sequence "S":

(0 * 2^2) + (0 * 2^1) + (1 * 2^0) = (1 * 4) + (0 * 2) + (1 * 1) = 5

We would refer to each 0 and/or 1 digit within a binary sequence as a "bit"

If we define the value of the bit as variable "b", and use variable "p" to refer to the position of each bit within the sequence, we can calculate the value of a specific term within the sequence with the mathematical expression (b * 2^p).

The series of the sequence is the actual decimal value of the binary number.

Since binary is read in a rightward-leftward manner, we could retrieve the decimal value of the binary sequence "010" in this manner:

(0 * 2^2) + (1 * 2^1) + (0 * 2^0)

As you may have noticed, the value of the exponent decreases as you read the expression in a rightward manner. This is consistent with my previous claim of binary being read in a right-to-left manner.

This sequence is also equivalent to:

"(0) + (2) + (0) = 2", assuming that we are referring to the base-ten counting system.

Hopefully this results in a wholesome and positive discussion.
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ParadigmaticAnon is not online. ParadigmaticAnon
Joined: 25 Jan 2016
Total Posts: 182
12 Feb 2016 10:38 PM
If any of the individuals participating has any further interest, I am willing to devise basic binary sequences that we can analyze collaboratively.
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ParadigmaticAnon is not online. ParadigmaticAnon
Joined: 25 Jan 2016
Total Posts: 182
12 Feb 2016 11:01 PM
Well then, I suppose that a computational example will garner interest.

Computers utilize binary sequences to store data. Each bit represents a specific instruction to be manipulated by components of the CPU.

This is accomplished by utilizing "0" and "1" to represent separate voltage states of a given segment of the hardware. "0" refers to low-voltage, and "1" refers to high-voltage.

Thus, imagine a sequence such as "01010101" as merely representing the computer sequentially reversing the voltage states of various signals within hardware gates. Each gate represents the basic logical operations of AND, OR, NOT, XOR.

Perhaps this will interest fellow users?
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ParadigmaticAnon is not online. ParadigmaticAnon
Joined: 25 Jan 2016
Total Posts: 182
13 Feb 2016 12:37 PM
I have developed another explanation for the users on the sub-section.

Suppose that we a machine containing six buttons. Each button can be successively activated/deactivated using a sequence of instructions. Each "button press" will reverse the button's current state. We can express this as a binary sequence of six bits.

This will be our representation:

000111

In the above sequence for our machine, the first three buttons are deactivated. The last remaining three buttons are active.

Naturally, since we are working directly with base-two, we can utilize logical operations to modify the behavior of the individual bits.

Let us define a function "P", which will represent each unique button press. Imagine that function "P" accepts an input "positional value", and signals a state change to the bit of that position. This would be our notation to use the sequence(Assuming that lowercase "p" refers to the position within the address and uppercase "B" refers to the actual memory address itself):

P(p) = ~B[p]

The "~"(Or logical NOT) operator merely reverses the numerical value of the bit found. In non base-two context, this would reverse "true" to false, and "false" to true.

Since base-two has only two valid digits, 0 and/or 1, this operator will likewise reverse 0 to 1 and 1 to 0.

Since our machine has six button, the function will need to be executed exactly six times to affect every digit.

Given that our original sequence was "000111", this is how it would be altered:

P(1) = 1

P(2) = 1

P(3) = 1

P(4) = 0

P(5) = 0

P(6) = 0

Altogether, the new button sequence would be "111000." Notice how the values of both sets of halves of the button sequence was swapped. Consequently, the first three buttons are activated. The last remaining three buttons are not.
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TotallyNotAnOTer is not online. TotallyNotAnOTer
Joined: 25 Jan 2016
Total Posts: 2094
13 Feb 2016 12:38 PM
EEEEEEEEEWWWWWWWWWWWWWWWW MATH BLEEEEEEEEEEEEEEEGGGGGGGGGGHHHHHHHHHHHH
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ParadigmaticAnon is not online. ParadigmaticAnon
Joined: 25 Jan 2016
Total Posts: 182
13 Feb 2016 12:41 PM
"EEEEEEEEEWWWWWWWWWWWWWWWW MATH BLEEEEEEEEEEEEEEEGGGGGGGGGGHHHHHHHHHHHH"

I can guarantee you that the "control" gained by being proficient in base-two manipulation will cause your mouth to salivate.

This is not necessarily "advanced" mathematics. It is merely just theoretical manipulation of a machine.
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BurnOfFlames is not online. BurnOfFlames
Joined: 04 Jul 2015
Total Posts: 4939
13 Feb 2016 12:49 PM
I remember this now...


I had learnt it from a computer textbook
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Replaced is not online. Replaced
Joined: 15 Jul 2009
Total Posts: 55335
13 Feb 2016 12:50 PM
uhhhh

i thought u just kept dividing the number by two to put it into binary lol

u make it seem complicated
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BurnOfFlames is not online. BurnOfFlames
Joined: 04 Jul 2015
Total Posts: 4939
13 Feb 2016 12:59 PM
Simple explanation


Binary = 101

Let's translate it into a number

1 = 2
0 = 1
1 = 0

1 * 2*2 + 0 *2^1 + 1 * 2^0

1 * 4 + 0 + 1

= 5

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iamjonroncinabon is not online. iamjonroncinabon
Joined: 10 May 2011
Total Posts: 9032
13 Feb 2016 01:02 PM
Does TheBinaryWolf count as a binary sequence?

Noot-noot
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BurnOfFlames is not online. BurnOfFlames
Joined: 04 Jul 2015
Total Posts: 4939
13 Feb 2016 01:06 PM
Let's translate 6 into a binary now

Number Quotient Remainder

6. 3. 0
3. 1. 1
1. 0. 1

Take 6, divide it by 2 and take the quotient to next row for further division, remember to write the reaminders to get the actual binary value.

Binary = 110
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ParadigmaticAnon is not online. ParadigmaticAnon
Joined: 25 Jan 2016
Total Posts: 182
13 Feb 2016 05:25 PM
"i thought u just kept dividing the number by two to put it into binary lol

u make it seem complicated"

Remember, we are not attempting to focus solely on methodologies. Rather, we are exploring the actual values that binary numbers represent. The process is much more rewarding when you can use a given skill to model logical solutions to seemingly difficult problems with computers.

BurnOfFlames provided an excellent technique for converting between bases. It would make a very nice iterative algorithm.
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