Binary numbers consist of only two digits, 0 and 1. This seems very inefficient and simple for us humans who are used to working in base 10, but for a computer base 2, or binary, is the perfect numbering system. This is because all calculations in a computer are based on millions of transistors that are either in an on position, or an off position. So there we have it, 0 for off, and 1 for on. But that on it’s own isn’t very interesting or useful. Having a switch that is either off or on tells us nothing and doesn’t allow us to do any maths at all, which after all is what we want computers for. In order to do anything useful we have to group our switches (called bits) into something bigger. For example, eight bits becomes a byte, and by alternating the position of the bits, either 1 or 0, we end up with 256 combinations. All of a sudden we have something useful we can work with. As it happens, we can now use any number up to 255 (we lose one because 0 is counted as a number) for our mathematics, and if we use two bytes, the number of combinations for our sixteen bits becomes 65,536. Quite staggering considering we’re only talking about sixteen transistors. Now, in modern computers, a CPU is likely to have anything up to a billion transistors. That’s 1000 million switches all working together at nearly the speed of light, and if we can count to sixty-five thousand with only sixteen transistors, then think what we can achieve with a billion. ut many people have forgotten the basics of the computer processor these days. To many it’s just a chip that you stick into a motherboard that makes it go. No thought is given to the sheer number of calculations that goes on inside a processor, even just to read the article you’re reading right now. This is probably because the size of these transistors are now so small, you actually need a microscope to see them, and they can be packed into a processor core so small, the wires that connect them all together are many times...

...BINARYNUMBER SYSTEM
Definition
The binarynumber 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 binarynumbers into decimal numbers. This will be explained in further sections.
Application
The binarynumber 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...

...4.3
4.3
Conversion Between Number Bases
169
Conversion Between Number Bases
Although the numeration systems discussed in the opening section were all base ten,
other bases have occurred historically. For example, the ancient Babylonians used 60
as their base. The Mayan Indians of Central America and Mexico used 20. In this
section we consider bases other than ten, but we use the familiar HinduArabic symbols. We will consistently indicate bases other than ten with a spelled-out
subscript, as in the numeral 43 five . Whenever a number appears without a subscript,
it is to be assumed that the intended base is ten. It will help to be careful how you
read (or verbalize) numerals here. The numeral 43 five is read “four three base five.”
(Do not read it as “forty-three,” as that terminology implies base ten and names a totally different number.)
For reference in doing number expansions and base conversions, Table 3 gives
the first several powers of some numbers used as alternative bases in this section.
TABLE 3
Selected Powers of Some Alternative Number Bases
Fourth
Power
TABLE 4
Base Ten
Base Five
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0
1
2
3
4
10
11
12
13
14
20
21
22
23
24
30
31
32
33
34
40
41
42
43
44
100
101
102
103
104
110
Base two...

...Pi has always been an interesting concept to me. A number that is infinitely being calculated seems almost unbelievable. This number has perplexed many for years and years, yet it is such an essential part of many peoples lives. It has become such a popular phenomenon that there is even a day named after it, March 14th (3/14) of every year! It is used to find the area or perimeter of circles, and used in our every day lives. Pi is used in things such as engineering and physics, to the ripples created when a drop of water falls into a puddle, Pi is everywhere. While researching this topic I have found that Pi certainly stretches back to a period long ago. The history of Pi was much more extensive than I originally imagined. I also learned that searching for more numbers in Pi was a major concern for mathematicians in which they put much effort into finding these lost numbers. The use for Pi was also significantly larger than I originally anticipated. I was under the impression that it was used for strictly mathematicians which is entirely not true. This is why Pi is so interesting.
The history of Pi dates back to a much later period than I thought. Ancient Egypt and Babylon are one of the first places that Pi was first founded. When discovered it showed that these ancient Pi values were within one percent of it's actual value, which is incredible considering the resources that weren't available yet like we have...

...Mathematics before Christ
Math started before Christ was born. Most of the time people use it, but they didn’t notice it. If you count how many sheep you have, that’s math. So when people use math, they didn’t know they were using it. The Romans used Roman Numerals and noticed math. So they know how to use it. That is where numbers got their name.
In Babylon and Egypt, the people first started using theoretical tools and numbering systems. The Egyptians used a decadic numbering system, which is based on the number 10 and still in use today. They also introduced characters used to describe the numbers 10 and 100, making it easier to describe larger numbers. Geometry started to receive great attention and served in surveying land, cities and streets. The Babylonians discovered the Pythagorean theorem. They understood it before Pythagoras was even born. The Babylonians also found out the approximate value of r^2. In India, Aryabhata calculated the number p to its fourth decimal point, managed to correctly forecast eclipses and, when solving astronomical problems, used sinusoidal functions.
As I woke up , I noticed that it’s unusually noisy outside our house. I clean myself up and ask my mom what was happening. Mom told me, ”Oh, they are making another pyramid. The pharaoh was found dead last night.” I thought to myself, that’s why its unusually noisy outside. Anyway, pyramids are made to honor the...

...should be named as A3Q2.c, etc. Make a folder, name it as (For e.g. 11K-2122_Sec(A)), place the source files for all the problems in this folder. The compressed folder should be submitted to slate. The program should be properly commented. Add your name and roll number at the beginning of each program, in comments. Plagiarism: Any sort of plagiarism is not allowed. If found plagiarized it will be graded 0 marks. __________________________________________________________________________________________
Q.1: Write a program that lets the user perform arithmetic operations on two numbers (integers). Your
program must be menu driven, allowing the user to select the operation (+, -, *, or /) and input the numbers. Furthermore, your program must consist of following functions: A) Function showChoice: This function shows the options to the user and explains how to enter data. B) Function add: This function accepts two numbers (integers) as arguments and returns sum. C) Function subtract: This function accepts two numbers (integers) as arguments and returns their difference. D) Function multiply: This function accepts two numbers (integers) as arguments and returns product. E) Function divide: This function accepts two numbers (integers) as arguments and returns quotient (double).
Q2: Write a program to take a depth (in kilometers) inside the earth as input data; compute and...

...Mrs. J. Buenaflor
English 101C- WB
10/04/12
Uncontrollable Numbers
Today, magazines are causing uproar with targeting consumers with outrageous numbers to gain attention. Seeyle states, “A trip to the newsstand these days can be a dizzying descent into a blizzard of numbers.” Reading through the article, the author adventured through numbers in sales, and how people can be addicted to these certain number strategies. She claims that in most popular magazine distribution all numbers sell.
Seeyle looks into most of many publications that are aimed at many women. “Service” publications’ in particular are always loaded with sex tips, exercise routines, and diet material surely aimed to catch the women’s eye. Seeyle announces that editors use catchy phrases and tips to get men’s attention too, not just targeting women. Seeyle warns many readers that thinking all these polls published in magazines can be mistakenly thought as interviews which disguise the real point behind all these popular magazines articles. The author then states, “Editors die to find the right combination of numbers to really improve sales that month, but mostly it all comes down to being a chance with the public”. Editors can work extra hard with numeral combinations but still may have trouble selling.
Seeyle also surprises readers with a thought that odd numbers are more believable then...

...to binary in a more attractive way
We all know how to convert decimal integral numbers to binary (don't we?) by the simple method of dividing succesively by 2 and using the remainders but what happens when we are trying to convert a decimal number which has a fractional part?
First we can see that it is obvious that the integral part of a decimal number will always be represented by an integralbinary (with no fractional part) while the fractional part of a decimal number will always be represented by a fractional part of a binarynumber (with no integral part). An integral number will be integral in any integral base and a fractional number will be fractional in any integral base. This means we can split a decimal number into its integral and fractional parts, convert them separately to binary and add them up again in binary. This means we can forget about the integral part and concentrate on converting the fractional part. Some decimal fractions may convert into binary exactly (like .5625) but others may not (like .5624) and we may get an infinite number of binary digits in the binary fraction.
One way of converting a decimal fraction to binary fraction is to first multiply it by a power of 2 so...

...Smith
Com 202
6 July 2008
Binary Code
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 binarynumbers 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...