Binary Number System

by Namrata Poladia

A binary number, also known as a base 2 number, is a number composed only of 0s and 1s. The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specifically inspired by the Chinese 1 Ching.

The base of a numbering system refers to the number of distinct symbols allowed in the system. In our daily life, we generally work with decimal numbers. The decimal system is the base 10 system as there are 10 distinct symbols allowed – 0 through 9. Why do computers not use the decimal system as well? Wouldn’t that be easier for the programmers as well? The answers to these questions lie in the architecture of the computers.

Any computer consists of a large number of digital transistors. The way these transistors are created, it is easiest to have them in the on or off state, rather than having 10 different states. The state of a single transistor is the smallest piece of information a computer can store. This is also called as a bit (similar to a digit for the decimal system). Larger units of information can be created by combining multiple bits together. From a mathematical point of view, any data that can be represented using decimal numbers can also be represented using binary numbers, just that the binary numbers are going to have more bits than the number of digits in the corresponding decimal number.

Concepts such as order and carry apply in the binary system same as how they apply in the decimal system. In the decimal system, a number consists of the ones digit, tens digit, hundreds digit, and so on. For example, in base 10 decimal:

Note that every digit represents a power of ten based on its position. Similarly, in the binary system, a number consists of ones bit, twos bit, fours bit, eights bit, and so on. That is, every bit represents a power of two based on its position. For example—a binary to a decimal (base 2 to base 10):

Decimal numbers and their binary representations:

Decimal Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000

 

Convert decimal numbers to binary

128= 64= 32= 16= 8= 4= 2= 1
56 1 1 1 0 0 0
131 1 0 0 0 0 0 1 1

Explanation:

56 = 32+ 16+8= 

131 = 128+ 2+1

add numbers where ones are there.

Computer memory units are typically represented in bytes. A byte consists of 8 bits. The typical metric system of measurements applies to bytes also, although in a slightly different manner. Similar to how a kilogram consists of 1000 grams of mass, a kilobyte (kB) is 2^10=1024 bytes. You can have a 200-word paper represented in a kB. A megabyte (MB) consists of 1024 kB or 2^20 bytes (slightly more than a million) and can store a small book. The next units are gigabyte (GB) (2^30 or slightly more than a billion bytes) which can store a typical movie, terabyte (TB) (2^40 or slightly more than a trillion bytes), petabyte (PB) (2^50 bytes).

Text

We learn how computers can store numbers but what about letters within a piece of text? How does a computer store a word like “school”? Whatever you read on any website, phone, tablet, and kindle is converted into binary numbers and stored. When storing text, each letter and symbol like a punctuation mark, a space, or even a new line, is assigned a specific number using ASCII coding standard. In ASCII, the letter A is represented by number 65, letter B by 66 and so on. The lowercase letters have different representations to avoid confusion. a=97, b=98, ...z=122.

Example: If you see “Hello” on your computer screen then computer finds its ASCII value and converts into binary numbers.

H e l l o
ASCII 72 101 108 108 111
Binary 1001000 1100101 1101100 1101100 1101111

There are more complex data types that need to be represented in computers.

Examples are numbers with a decimal point (12.34), photos, videos, etc. Every different type of data has a standard encoding system that makes is easy for humans to work with computers. But ultimately, everything gets converted into zeros and ones. The tiny bits are very powerful indeed.

 

 

What is the English Language and Literature at WA Preparatory School? Why do we read Classical Literature?

By Perry Sein
August 7, 2020

In the Washington Preparatory School's English Language and Literature course, we strive to acquire the linguistic aspects of the English language and skills needed for reading, writing, analyzing, interpreting, and evaluating literary and non-literary texts in the English language. We also endeavor daily to learn the valuable lesson imparted through classical literature.

Language is "alive" in that many new words are "born," constantly, especially in the science and technology fields. They are added to our list of vocabulary, whether we are aware of them or not, and new forms of electronic media, stories, fiction, and non-fiction works are produced every day.

Why then are our WA Prep students and, for that matter, students in English classes worldwide, are still reading, analyzing, and interpreting classic "old" literature instead of reading some random morning Tweets or paperback pop fiction? Because literature, as opposed to popular fiction, is a work of art that has depth, meaning, lasting value, and teaches life lessons.

Literature is worthy of analysis, criticism, discussions, and introspection. Literature requires careful thinking, reflecting, and inquiring. Our courses follow an IB inquiry-based learning model that encourages our students to choose literature based on their knowledge and interest and emphasizes learning how to learn, and how to do research, using both traditional and contemporary media.

Classic literature, poetry, and stories evoke, stir, challenge our values, perspectives, and actions. Classic literature addresses universal human concerns, and it will challenge, change, or shift our thinking and views on life. And world literature we study in our class is a silken cord that connects all humans in the world and about being open-minded, a characteristic of the IB learner profile.

Classical literature also has merit, which is continually respected and examined by experts and critics throughout the years. Classic literature is alive in all English classes around the world, and the English teachers in schools bear the sole responsibility and the risk of selecting and teaching literature, albeit at the risk of disapproval and sometimes outright rejection of individual books.

Our students at Washington Preparatory School's English Language and Literature course continue to read, analyze, interpret, and discuss literature. Through literature, we learned about how selfishness and unbridled ambition led to the tragic death of Macbeth by William Shakespeare, first performed in 1606. We learned about fighting racial injustice and courage by analyzing To Kill a Mockingbird by Harper Lee, published in 1960. Moreover, we learned about the dangers of the police state, censorship, and the truth, when all Clarisse McClellan did, was to ask Guy Montag, "Are you happy?" in Fahrenheit 451 by Ray Bradbury, first published in 1953.

Classic literature will outlast us; it has survived our forefathers and their forefathers so far.

Although we continue to make advances in science and technologies, we are still short on understanding and improving our basic pitfalls in human nature to build a better world where all humans can live in harmony. We hope that the hard lessons and the values imparted through classical literature are learned and not repeated despite our advancement of science and technology in our world.

Citations:

https://www.merriam-webster.com/words-at-play/new-words-in-the-dictionary

https://www.whatisib.com/inquiry-based-learning.html

https://www.thompsonschools.org/Page/15352

https://www.themantle.com/literature/what-makes-classic-basics

https://www.britannica.com/art/literature

https://www.enotes.com/homework-help/why-study-literature-important-what-skills-do-408329

 

 

 

Laura Granger (Mathematics Teacher)
August 27th, 2020
Encryption, Decryption, and Matrices

 

Over the course of my 20 years teaching mathematics, matrices have been in and out of the Algebra 2 and Pre-Calculus curriculum. I happen to love working with and teaching matrices, so I was happy to see them back in our Pre-Calculus/Pre-IB curriculum last year. After mastering the processes and problem solving uses of matrices, my students completed an encryption project using matrices. This project uses matrices and cryptography to code and decipher secret messages. See if you can unlock the code and decipher their secret message!