The first known occurrence of the binary numeral system is around the 8th century BC. It was created by the ancient Indian writer Pingala. He came across this as a method to describe prosody. This type of numeration system is a descendant of the Old Kingdom’s Eye of the Horus. A full set of eight trigrams and sixty four hexagrams, which are analog to the three bit and six bit binary numerals, are known to the ancient Chinese as I Ching. The Chinese scholar Shao Yong developed values for binary numbers 0-63 in the I Ching hexagrams arrangement. In 1605 Francis Bacon introduced a system by which letters of the alphabet could be reduced to sequences of binary digits.

He added that this method could be used with any objects at all: "provided those objects be capable of a twofold difference only; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature". In 1854, British mathematician George Boole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra. His logical calculus was to become instrumental in the design of digital electronic circuitry. (First and second paragraph come from the history of binary code found on Wikipedia, http://www.wikipedia.com)

Binary meaning two. The principle behind digital computers. All input to the computer is converted into binary numbers made up of the two digits 0 and 1. The bits are stored as charged and uncharged memory cells or as microscopic magnets on disk and tape. Display screens and printers convert the binary numbers into visual characters. The electronic circuits that process these binary numbers are also binary in concept. The current flowing through one switch turns on (or off) another switch, and so on. A computer's capability to do work is based on its workspace capacity (memory), storage capacity...

...The modern binary number system, the basis for binarycode, was discovered by Gottfried Leibniz in 1679 and appears in his article Explication de l'Arithmétique Binaire. The full title is translated into English as the "Explanation of the binary arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi."[1] (1703). Leibniz's system uses 0 and 1, like the modern binary numeral system. Leibniz encountered the I Ching through French Jesuit Joachim Bouvet and noted with fascination how its hexagrams correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.[2][3] Leibniz saw the hexagrams as an affirmation of the universality of his own religious beliefs.[3]
Binary numerals were central to Leibniz's theology. He believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing.[4] Leibniz was trying to find a system that converts logic’s verbal statements into a pure mathematical one. After his ideas were ignored, he came across a classic Chinese text called I Ching or ‘Book of Changes’, which used a type of binarycode. The book had confirmed his theory that life could be...

...1435
>> 4-BIT BCD CODES
>> 6-BIT BCD CODES
>> 8-BIT BCD CODES
>> ZONED-DECIMAL & PACKED DECIMAL
FORMATS
INTRODUCTION
HOW DOES A COMPUTER REPRESENT THE NUMERICAL DATA IN
BINARY FORMAT?
Base-2 digits [Straight Binary]
BCD [Binary-Coded Decimal]
binary-coded decimal (BCD) - class of binary encodings of decimal
numbers
In byte-oriented systems (i.e. most modern computers), the term
uncompressed BCD usually implies a full byte for each digit
(often including a sign), whereas packed BCD typically encodes two decimal
digits within a single byte by taking advantage of the fact that four bits are
enough to represent the range 0 to 9.
uncompressed BCD
Decimal
Binary
0000
9
1001
0000
1
0001
packed BCD
Decimal
Binary
9
1001
1
0001
In BCD, a digit is usually represented by 4 bits which, in general, represent the
values/digits/characters 0–9.
Types of 4-bit BCD formatted codes
>>Weighted 8-4-2-1 BCD Codes
>>Weighted 4-2-2-1 BCD Codes*
>>Non-weighted XS-3 BCD Codes
Excess-3 was used on some older computers as well as in cash
registers and hand held portable electronic calculators of the 1970's,
among other uses. It is a way to represent values with a balanced
number of positive and negative numbers using a pre-specified
number N as a biasing value. It is a nonweighted...

...sorted.
Therefore, the binary search is implemented.
Function of the binary search:
1)
Considering that the structure is already sorted (if not we need to do so)the goal of the binary search is to find a location within the “tree” called the key, and ensure, that there is space for it if something were to be overwritten on it.
The binary search functions by looking through the whole length of the data structure (it finds the range between the maximum and minimum, as well as the average between the highest and lowest values and divides them by two to get the midpoint of the values, the middle component). If the value being searched for is higher than the midpoint, then it goes into to the middle of the lower quartile of the array and looks again. If the middle components's stored value was too low, it will go to the upper quartile of the array instead. The search keeps repeating this 'split the remainder' step until it finds the “key (the value you want) and if it misses it, it will simply return -1, knowing that that value that we searched for doesn't exist within the specified length of the array.
On the other hand, if A → B works, within a binary search tree, according to the boolean logic that it is built upon, then if A→B then B→A must be also true, because of the “recursive” nature of the structure of the binary tree in itself.
And so, the “reverse algorithmically...

...Gray Code
This is a variable weighted code and is cyclic. This means that it is arranged so that every transition from
one value to the next value involves only one bit change. The gray code is sometimes referred to as
reflected binary, because the first eight values compare with those of the last 8 values, but in reverse order.
The gray code is often used in mechanical applications such as shaft
DecimalBinary Gray
encoders.
Modulo 2 Arithmetic
0
0000 0000
This is binary addition with the carry ignored.
1
0001 0001
Converting Gray Code to Binary
A. write down the number in gray code
2
0010 0011
B. the most significant bit of the binary number is the most significant bit of
3
0011 0010
the gray code
C. add (using modulo 2) the next significant bit of the binary number to the
4
0100 0110
next significant bit of the gray coded number to obtain the next binary bit
5
0101 0111
D. repeat step C till all bits of the gray coded number have been added
modulo 2
6
0110 0101
the resultant number is the binary equivalent of the gray number
Example, convert 1101101 in gray code to binary
Gray
1.
2.
3.
4.
3/4
3/4
3/4
3/4
Binary
1101101
1101101 1 copy down the msb
1101101 10 1 modulo2 1 = 0...

...BINARY NUMBER SYSTEM
Definition
The binary number system is relatively simple because it only uses two digits, 0 and 1. Therefore, it has a numerical base of 2. In order to count further than 1, we simply start back at 0 and add to the number on the left.
Decimal
Binary
0
0000
1
0001
2
0010
3
0011
4
0100
5
0101
6
0110
7
0111
8
1000
9
1001
The powers of 2 are used to convert binary numbers into decimal numbers. This will be explained in further sections.
Application
The binary number system is also called the language of computers. They are very important in the field of electrical engineering and computer sciences. The binary digits are used to operate transistors which can be found in most electrical devices. The 0 digit means that there is no current flowing, while the 1 digit means that there is a flow of current. Using this, it can turn on and off various signals in order to control the computer or electrical device.
Operations
Addition
Binary addition is very much like decimal addition. It has only two digits, making it much easier to work with. The possible combinations and answers are listed on the table.
Addend 1
Addend 2
Sum
0
0
0
0
1
1
1
0
0
1
1
1 with a carry of 1
Subtraction
Since subtraction is merely the opposite of addition, the rules to be followed closely resemble each other. The rules of...

...Code of Ethics Comparison Paper
Melissa J. Diehl
Liberty University
September 2, 2012
Abstract
Different organizations are driven by specific sets of code of ethics, which are used to protect many different aspect of the organizations, specifically the client, counselor, and organization. Concerning the standards of a counselor, their ethics are not only provided by the laws of the state or their practice, but also outside sources who present basic values and regulations of ethical standards in their code of ethics. This paper will look at two specific associations: the American Counseling Association (ACA) and the American Association of Christian Counselors (AACC). The purpose of this paper is to discuss both the similarities as well as differences of these two organizations and their standards of ethics. While discussing the AACC and ACA organizations standards, this paper will also look at three specific areas which we chosen to compare and contrast: confidentiality, fees, and competence.
ACA and AACC Code of Ethics Comparison
The ACA and AACC codes of ethics were put into practice to protect the client, counselor, and organization. The ACA code of ethics was put into practice in 2005 with the mission to promote the development of...

...assignment)
----- This is the end of your Drop/Add Period -----
Your dedication to the class is very important to your success.
If you are behind-pace at this point, you will be withdrawn.
Week 3
02.03 Cell Structure & Function (read lesson, take notes, do assignment)
02.04 Cellular Energy (read lesson, take notes, do assignment)
02.05 Cellular Respiration (read lesson, take notes, do assignment)
Week 4
02.06 Intro to Photosynthesis (read lesson, take notes, do assignment)
02.08 Module 2 DBA (call teacher for open-notes discussion)
02.08 Module 2 Exam (take exam using password from teacher)
Week 5
03.00 Module 3 Pretest (skim checklist, do pretest)
03.01 The Cell Cycle & Mitosis (read lesson, take notes, do assignment)
03.01 Binary Fission and Mitosis Honors (read, notes, assignment)
03.02 Meiosis (read lesson, take notes, do assignment)
Week 6
03.03 Mendel (read lesson, take notes, do assignment)
03.04 Heredity Patterns (read lesson, take notes, do assignment)
Week 7
03.05 DNA Replication (read lesson, take notes, do assignment)
03.06 Mutations (read lesson, take notes, do assignment)
Week 8
03.07 Biotechnology (read lesson, take notes, do assignment)
03.08 Health and Genetics (read lesson, take notes, do assignment)
03.10 Module 3 DBA (call teacher for open-notes discussion)
03.10 Module 3 Exam (take exam using password from teacher)
Week 9
04.00 Module 4 Pretest (skim checklist, do pretest)
04.01 Ecology (read...

...The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers.
Why Computers Use BinaryBinary numbers – seen as strings of 0's and 1's – are often associated with computers. But why is this? Why can't computers just use base 10 instead of converting to and from binary? Isn't it more efficient to use a higher base, since binary (base 2) representation uses up more "spaces"?
I was recently asked this question by someone who knows a good deal about computers. But this question is also often asked by people who aren't so tech-savvy. Either way, the answer is quite simple.
A modern-day "digital" computer, as opposed to an older "analog" computer, operates on the principle of two possible states of something – "on" and "off". This directly corresponds to there either being an electrical current present, or said electrical current being absent. The "on" state is assigned the value "1", while the "off" state is assigned the value "0".
The term "binary" implies "two". Thus, the binary number system is a system of numbers based on two possible digits – 0...