Speaking Computer: The Binary Words of Technology
I’m going to make a guess about you. Yes, YOU. I don’t know you, but I know one very important thing, you’re reading this page. I’ll go one step further with my guess, you’re reading this page on a computer, perhaps a phone, tablet, or laptop, but some kind of computer. Now, you’re reading this page in English, I suppose I just made another guess about you. And this page is composed of select letters within the 26 letter alphabet. Those 26 letters are mixed together by predetermined rules to form more complex words.
Now, like I said, you’re reading these English letters on a computer. Your computer is a complex machine developed by many smart people over a few years. Certainly, 26 letters wouldn’t be an issue for such an innovation? Well, it is.
Computer language is very much different than our own, because, while we use 26 letters, computers use just 2 numbers. That’s right, computers communicate only using 0 and 1.
Read this sentence in English.
Simple right? This is how your computer sees that same sentence:
01010010 01100101 01100001 01100100 00100000 01110100 01101000 01101001 01110011 00100000 01110011 01100101 01101110 01110100 01100101 01101110 01100011 01100101 00100000 01101001 01101110 00100000 01000101 01101110 01100111 01101100 01101001 01110011 01101000 00101110.
That five word sentence easily becomes nearly impossible to read, every 8-number section of the above sentence (01010010) is a new letter.
How can computers communicate, work, calculate, and function with such gibberish?
Well, to tell that story, we’ll need to visit the 17th century.
A German mathematician by the name of Gottfried Wilhelm Leibniz developed a 2-base number system in 1679 (“Binary system.”). He published his findings in 1703 in his article titled, Explanation of binary arithmetic, which uses only characters 0 & 1; with remarks about its utility and the meaning it gives to the ancient Chinese figures of Fuxi (Garfinkel and Grunspan 32). (Try saying THAT title 10 times fast).
Our standard numbering system is base-10, meaning we use 10 numbers (0–9). These numbers form the base of every other number. But Gottfried developed an entirely new numbering system, his was base-2, meaning he used two numbers (0–1). With these two numbers, all other numbers were created and represented. With his new system, Gottfried avoided nearly all multiplication tables (see they aren’t THAT important) and created simple rules for calculation (Garfinkel and Grunspan 32). His numbering system was called binary, because it used two numbers.
Let’s review a few simple problems and discover how the numbering system works.
Each number is represented by a combination of 0s and 1s. Of course 0 is represented by 0 and 1 is represented by 1.
For larger numbers, we run into some complications, but let’s review how base-2 works.
Base-2 starts at 0, then doubles every number after that, therefore it could be written in this way:
0, 2, 4, 8, 16, 32, 64, 128, etc.
Or written another way:
2(^0), 2(^1), 2(^2), 2(^3), 2(^4), 2(^5), 2(^6), 2(^7)
As you can see, the base remains 2, and the power that each 2 is raised increases by 1, doubling each number. This forms the foundation of the binary numbering system. Now let’s explore how to represent a number in binary. Whenever I convert base-10, or decimal numbers, to binary I like to start with a quick table (this makes the process easy and quick on paper). Write out a table as follows:
Now let’s convert the number 55, into binary. We will start by finding the largest number that can be subtracted from 55 in the table. That number is 32. So we’ll place a 1, in the box under 32.
55–32 = 23. Now we do the process again. 23–16 = 7. We’ll place a 1 underneath 16.
8 doesn’t fit into 7, so we’ll enter a 0 under the 8.
7–4 = 3. We’ll place a 1 under 4.
3–2 = 1, Place a 1 under the 2.
And since 1–1 = 0. We’ll place a 1 under the 1 and 0’s everywhere else, and we’re done!
Our binary number is 00110111 which is equal to 55. To convert the number back to 55, simply reverse the process. Fill the table in with the binary number and add all the places where there is a 1. Therefore, 1 + 2 + 4 + 16 + 32 = 55.
Now, let’s consider a simple math problem using binary. Math with binary numbers is even easier than decimal (or base-10 numbers). Let’s add 55 to 10. 10 is 00001010 and 55 is 00110111. Our problem is 00110111 + 00001010. It’s the same as regular addition, but remember, you only get to use 0s and 1s.
Now let’s add. Start from the right. 1 + 0 = 1.
We’ve hit a snag. I encountered 1 + 1, which is 2 in decimal, but we can’t use 2, but we can use 2 in binary which is 10. So add and carry (write 0 underneath and carry the 1.). We’ll continue that same process and solve the problem.
So, our answer is 01000001. We can check our answer by plugging in into our table:
Now, we add the columns which have 1s. So, 64 + 1 = 65. We know that 55 + 10 = 65. So our answer is correct! Subtraction is carried out in the same way, just reverse. Division and multiplication are done in the same way as regular numbers as well.
So that’s binary in a nutshell.
But why is it so important and why is binary the only language of computers?
Well, at their core computers control electricity. When you send an email, the computer is only sending pulses of electricity. Really, computers are simply switches that control electricity. We’ll explore this concept more in future blogs (so be sure to follow me here on Medium).
Now think about a light switch. When you turn the switch to “ON” electricity flows to the bulb and the light comes on. When you switch it to “OFF,” electricity stops flowing and the bulb turns off. That’s how a computer works. But a computer is made of billions of tiny, microscopic transistors. Each transistor is a switch.
When you turn on your light, there are two options, ON and OFF.
There is nothing in the middle or onish or offish positions. It’s ON or OFF.
The same is true for transistors. They are either on or off, nothing in between. In binary, 1 represents ON and 0 represents OFF. So, when we see the binary number, 00110111, the computer turns transistors off, off, on, on, off, on, on, on. Now, this may seem confusing, you can’t turn a switch off, that’s already off. But computers work in cycles, so each cycle could be ON or OFF. When we see, off, off, the transistor is off for two cycles (sending no pulse of electricity), then on for two cycles (send one pulse for each cycle), etc.
Computers use the ON and OFF nature of transistors represented through binary for everything.
Every number, letter, shape, and even color on your screen has a binary translation. This is simple to understand with numbers, but how does binary represent this vast collection of information, including letters? During the early days of modern computing (less than one hundred years ago) when researchers wanted to build computers for more than calculation, computer scientists discovered this issue. They developed a system of codes to represent all information in the form of binary numbers.
One such method that isn’t as popular today, is ASCII, which stands for “American Standard Code for Information Interchange.” The ASCII table lists letters, uppercase and lowercase, numbers, and some symbols, with number codes that can be converted into binary. For example, capital letter A is ASCII code 65 which converts to 01000001 in binary. Each letter is 8 digits long. Let’s look at a quick example of the word HELLO.
H is 72 in the ASCII table or 01001000 in binary. E is 69 or 01000101. L is 76 or 01001100. O is 79 or 01001111.
So, the word HELLO is 01001000 01000101 01001100 01001100 01001111 in binary.
Of course, we humans don’t use binary. That’s where the computer’s operating systems (such as Windows) and programming languages (such as Java) are used. The computer converts the information into binary by itself in a process called compiling.
In binary we call each digit a bit (binary digit). And each grouping of 8 bits is called a byte. These bits and bytes are the primary measurements for the storage systems of a computer. I’m sure you’ve heard of a gigabyte when using a USB stick or maybe an external hard drive or when you bought a laptop. 1 gigabyte is about 1,000,000,000 (1 billion) bytes and about 8,000,000,000 (8 billion) bits.
In 1703, when Gottfried Leibnix published his article on binary arithmetic, he could never have dreamed of its use.
But binary has become the language of our world, even if none of us ever use it, see it, or speak it. Binary’s 0s and 1s power many of our homes, our TVs, smart watches, phones, computers, cars, and much, much more. Binary arithmetic is the ninth major milestone in the history of computing.
More on the Importance of Math:
More on the History of Computers:
Works Cited
“Binary and Hexadecimal Number Systems.” Khan Academy, Khan Academy, www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/binary-multiplication.
“Binary Number System.” Math Is Fun, www.mathsisfun.com/binary-number-system.html.
Bogomolny, Alexander. “History of the Binary System.” Interactive Mathematics Miscellany and Puzzles, www.cut-the-knot.org/do_you_know/BinaryHistory.shtml.
Garfinkel, Simson, and Rachel H. Grunspan. The Computer Book: from the Abacus to Artificial Intelligence, 250 Milestones in the History of Computer Science. Sterling, 2018.
Gross, Melanie. “The Importance of Binary Numbers in Computing — GHacks Tech News.” GHacks Technology News, 7 May 2012, www.ghacks.net/2011/08/12/the-importance-of-binary-numbers-in-computing/.
Injosoft AB. “ASCII Code — The Extended ASCII Table.” ASCII Code — The Extended ASCII Table, www.ascii-code.com/.
Porubsky, Stefan. “Binary System.” BinarySystem, www.cs.cas.cz/portal/AlgoMath/NumberTheory/Arithmetics/NumeralSystems/PositionalNumeralSystems/BinarySystem.htm.
