Ones and Zeros, the Magic Heroes that Make the World Go ‘Round.
The term binary keeps coming up in pop culture, from gender related topics to political parties to computing. Binary is all the rage these days, and rightfully so, as it’s the language of computers. And we all know, computers pretty much power the world these days. But what does the term binary mean, and what the heck are binary numbers? Binary means consisting of, indicating, or involving two. When people talk about binary as a gender issue, they’re basically arguing the fact that gender is either binary (meaning there are only two genders), or that gender is not binary( meaning there are more than two genders). In math, binary refers to how we count. Our regular, plain vanilla, western-standard for counting involves a system related to tens, we call that base-10. Binary is much simpler, it uses only 0’s and 1’s, making it base-2. If that sounds confusing, don’t worry. We’ll cover what that means in a bit. But first, a puny joke about binary.
Stop me if you’ve heard this one…
If you get that joke, chances are you’ve heard it so many times it’s lost its humor. However, if you’re like I was, this joke makes no sense.
Spoiler alert: this is where I break it down and explain the joke. The reason it was confusing to me is because I first read it as: There are only ten types of people in the world... Read that way, the joke seems to be missing 8 other types of people (thus the joke). In binary, we don’t have the number ten, we only have ones and zeros. The correct way to read the joke is:
There are only one zero types of people in the world...
I don’t know who to credit for this little piece of comedic gold, however I have tracked down the man responsible for modern binary. Gottfried Wilhelm Leibniz, the mathematician, philosopher, and man of many talents. He was one of the creators of geology, he co-created calculus, as well as developing the humble little binary number system. Even though our friend Gottfried gets all the credit for coming up with binary back in 1679, there’s evidence of the ancient Egyptians using two symbol counting in their hieroglyphics (binary history). Holy crap, binary is hella old.
If binary has been around since the beginning of early civilization, why isn’t it the dominant form of counting today? Well first of all, we humans have ten fingers. Counting to ten on our hands is as natural as it gets. That is, if you have been blessed with five fingers on each hand. Another added bonus is that incrementing by 10 is really easy and takes up very little space to store really large numbers. While this is a handy trait for writing, it doesn’t translate well to computing. For as long as I can remember I’ve been hearing that computers only speak binary. I had no idea what people meant by that until recently. Computers don’t actually speak any languages by the way, not in the same way humans and other species do. What they do instead, is store electrical signals as information. A high voltage electrical signal is “on” stored as a 1, and a low voltage electrical signal is “off”, stored as 0. How does that relate to binary numbers? Let’s compare decimal numbers (base-10) to binary and see if this makes more sense.
Base Numbers and Number Systems
A base number is the basis of a place value number system. Successive powers of the base number are used for each column. The decimal system uses 10 as its base number so it is called a Base-10 system. The binary system uses 2 as its base number so it is called a Base-2 system.
In Base-10 we start with 0, and then 1, 2, 3…and we keep going until we get to 9. Once we get to 9, we add a one on the left side of the 9, and start the right hand number back at zero. When we get to 19, we increase the left side by one, start the righthand number back at zero, and repeat this process. If you count the symbols we use to represent each digit, we have ten. This is why the decimal system is referred to as base-10.
Binary System
Binary is a number system using the base number 2. Most computers and other electronic devices use the binary system. Binary numbers are written using the digits 0 and 1 to express each number. Binary digits are called ‘bits’.
example of binary to decimal: 1100 = 12
How to Convert a Decimal Number to Binary
Analyzing any number is very easy, here how it works. Get a piece of paper and draw a table that is 8 across, and 3 down.
Across the top row from right to left, fill in the powers of 2 starting with 2 to the zeroth power, ending with 2 to the seventh power on the far left. In the middle row, calculate the value. Example: 2 to the second power = 4. A few rules to keep in mind: 2 to the zeroth power = 1, because any number to the zeroth power is 1, 2 to the first power = 2, because any number times 1 is that number. Keep filling in the rest of the values by multiplying the last result by 2. You should have 128 under 2 to the seventh power. If you got a different result perhaps go back and check your work. The bottom row we’ll fill in as we convert from decimal to binary.
Next we analyze the number we are converting to binary. For this example I will use the number 75.
Start by comparing the value in the column on the farthest left. Does the value (128) fit in your number? The reason you check this, is because it helps you know if it is a 1 or a 0. Since 75 is less than 128, we write a 0 under 128. Another way to look at it is that 128 fits into 75 zero times. Next we look at 64, does that fit into 75? Since it does, we write in a 1 under 64, then subtract 64 from 75 (75-64 = 11). Next we look at 32, does this fit into the remainder of the last operation? Since 11 is less than 32 we write a zero under 32 and go to the next value. Does 16 fit into 11? Nope…write a zero. How about 8? It does, so we subtract (11-8 = 3) and write a 1 in the 8 column. I’ll let you finish this problem. If you didn’t get zero when you got to the 1’s column, you made an error and you should go back and check your work.
Did you come up with the same result as me? I got 01001011 = 75. Since there is a leading zero, we can simplify our result as say 1001011 = 75. Here is a handy web application that you can use to check your results.
Binary Number’s computer significance
So now that we know how to convert decimal numbers to binary, how does this all relate to computers, and why do computer scientists study binary?
Computers use binary — the digits 0 and 1 — to store information. A binary digit, or bit, is the smallest unit of data in computing. It is represented by a 0 or a 1. Binary numbers are made up of binary digits (bits), eg our old friend the binary number 1001011.
The circuits in a computer’s processor are made up of billions of transistors. A transistor is a tiny switch that is activated by the electronic signals it receives. The digits 1 and 0 used in binary reflect the on and off states of a transistor.
Computer programs are sets of instructions. Each instruction is translated into machine code — simple binary codes that activate the central processing unit. Programmers write computer code and this is converted by a translator into binary instructions that the processor can perform. Pretty cool huh?
Conclusion
All software, music, documents, and any other information that is processed by a computer, is also stored using binary. When you are using Twitter, Facebook, Google, you are typing in your native language, but the computer stores your friends, and images, and events in binary. We humans are social creatures. Without our social networks life can feel lonely. Thankfully we have social media to help us stay connected to our friends and family. In these modern times, computers are as much a part of our lives as our friends. We bank online, we socialize online, and we experience a lot of the world with the aid of computers. I cannot image a world without computers, and the binary system that drives them.
