Dear Mathman,
I heard this joke in math class the other day:
“There are only 10 types of people in this world- those who understand binary and those who don’t.”
I’m one of the types of people who doesn’t get it. Please help.
Thanks,
Sly T. Lee Confused
Dear Sly,
Thanks for asking for help. That is a great skill more of us need to use. BTW, you sure know how to tell a joke. I just had to pick myself up off the floor. I laughed myself right out of my chair. Keep them coming.
Anyways, this joke revolves around understanding the binary system. You might not realize it, but we both needed the binary system to even see this blog entry. Huh? As a matter of fact, you’re using the binary system anytime you use anything powered by electricity. Anything.
The binary system is based on the prefix “bi”. Do you know what number “bi” is referring to? Hint: think bicycle. I hope you figured out “Bi” means “two”. So the binary system is counting system based on the number 2. A bit lost? Let’s go back to the electricity example for a second. . Think about the common light switch. There are only two options, on or off. The electricity flows or it doesn’t (we’re ignoring dimmer switches to keep it simpler).
Any electronic device is broken down into a whole lot of light switches that are on or off. Fortunately for us, many of these switches have been shrunken down to a microscopic level. If they hadn’t, this computer that I’m typing on would take up a fair amount of real estate here in Mathopolis. Ah, the wonders of modern science.
Enough of science, let’s get back to math:
We’re not used to the simplicity of the binary system, we’re used to a much more complex system of keeping track of numbers. Our system is base 10 and is called the decimal system. It’s worth it to think about this for a minute so we can understand and appreciate the binary system a bit more. The decimal system revolves around 10 possibilities for each digit (single number). You know these possibilities as 0,1,2,3,4,5,6,7,8, and 9 (that was fun to type from the top of the keyboard). We know the place values in our system as “ones”, “tens”, “hundreds”, “thousands”, “ten thousands”, and so on. Think of a number to keep this straight:
67,890 is 6 ten thousands, 7 thousands, 8 hundreds, 9 tens, and 0 ones.
In our decimal system the number 10 is made up of 1 tens and 0 ones. When we write a number we start with the lowest value for a digit, 0, and work our way through the digits until we get to the highest value, 9. If we have to go higher than 9 we add the next place value and use a 0 to hold the first place value. We’re so used to doing this automatically we don’t think about it anymore.
The binary system works the same way. We start with a 0 in the first place value and count up until we hit the largest digit, then we add the next place value and start over. So, the number 0 in binary is 0. The number 1 in binary is 1. The number 2 in binary exceeds the highest digit for first place value so we need to add the second place value.
In base 2 (binary), the number 2 is written as 10. The place values go ones, twos, fours, eights, and so on. In the decimal system the place values are: 10^0=1, 10^1=10, 10^2=100, 10^3=1000, and so on. In the binary (base 2) system, the place values are: 2^0=1, 2^1=2, 2^2=4, 2^3=8, and so on. You count the same: 1,2,3,4,5,6,7,8,9,10,11, etc. but the numbers are written differently. This is like a foreign language for math.
Now, take a moment and reread the joke. Is it funny yet? If we wrote it without the 10 in binary, which really is the counting number 2, it wouldn’t be nearly as funny:
“There are only 2 types of people in this world- those who understand binary and those who don’t.”
Stay radical,
Mathman