The ELA Connection for this project is an argumentative essay on the importance of binary numbers and their use in everyday life:
On the Importance of The Binary Numerical System
Binary 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"?
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 and 1. This is where the strings of binary digits come in. Each binary digit, or "bit", is a single 0 or 1, which directly corresponds to a single "switch" in a circuit. Add enough of these "switches" together, and you can represent more numbers. So instead of 1 digit, you end up with 8 to make a byte. (A byte, the basic unit of storage, is simply defined as 8 bits; the well-known kilobytes, megabytes, and gigabytes are derived from the byte, and each is 1,024 times as big as the other. There is a 1024-fold difference as opposed to a 1000-fold difference because 1024 is a power of 2 but 1000 is not.)
On first glance, it seems like the binary representation of a number 10010110 uses up more space than its decimal (base 10) representation 150. After all, the first is 8 digits long and the second is 3 digits long. However, this is an invalid argument in the context of displaying numbers on screen, since they're all stored in binary regardless! The only reason that 150 is "smaller" than 10010110 is because of the way we write it on the screen (or on paper). Increasing the base will decrease the number of digits required to represent any given number, but taking directly from the previous point, it is impossible to create a digital circuit that operates in any base other than 2, since there is no state between "on" and off.
"Imagine a computer based on base-10 numbers. Then, each "switch" would have 10 possible states. These can be represented by the digits (known as "bans" or "dits", meaning "decimal digits") 0 through 9. In this system, numbers would be represented in base 10. This is not possible with regular electronic components of today. Is this system more efficient? Assuming the "switches" of a standard binary computer take up the same amount of physical space (nanometers) as these base-10 switches, the base-10 computer would be able to fit considerably more processing power into the same physical space.
Binary numbers first arose around the 4th century in the great Vedic literature's and were written in the first language ever devised, Sanskrit. However, over time, the numerical system was eventually forgotten about, until it was rediscovered in the 17th century.
In 1679, German mathematician Gottfried Leibniz, the father of calculus, published an article titled "Explanation of the Binary Arithmetic", in which he spoke of a numeral system consisting of only the digits 0 and 1. He was theorizing that life could be reduced to simple codes of rows of combinations of zeroes and ones. Not actually knowing what this system would be used for, eventually, with the help of George Boole, Boolean logic was developed, using the on/off system of zeroes and ones for basic algebraic operations. The on or off codes were rapidly implemented by computers for doing seemingly unlimited numbers of applications.
Today, the binary numerical system is the foundation for all modern electronics. Using only two digits, 0 and 1, any number can be represented. This is extremely useful in computing, where memory consists of small elements that may only be in two states, on and off, or 0 and 1. Such elements are known as binary digits, or bits. Four bits combine to make a byte, which can be used to store all kinds of data, from pictures and videos, to text and audio.
We only use binary because we currently do not have the technology to create "switches" that can reliably hold more than two possible state. The binary system was chosen only because it is quite easy to distinguish the presence of an electric current from an absence of electric current, especially when working with trillions of such connections. And using any other number base in this system ridiculous, because the system would need to constantly convert between them.
All computer language is based on the binary system of logic. It is the back end of all computer functioning. All computer functions will rapidly toggle between 0 and 1 at rapid speeds. By doing so, computers have come to assist humans in tasks that would take so much longer to complete. For example, in WWII, the United States sent sensitive war plans and other information to their allies after encrypting the information, which was done by humans. Encrypting information usually took an extensive amount of time to do, and without the encryption code, it was nearly impossible to decode. Today, computers have come to replace humans in the field of cryptography and many others because they can do seemingly impossible or extremely tedious tasks quickly.