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QUICK! What's 2^12? No Cheating!

If you guessed 1024, you're wrong. :) I was just asked this question not 20 minutes ago, and I choked, when the answer was in my hands, quite literally.

I've blogged about this before, but counting in binary is easy, just using your fingers. So, when asked that question, the calculator that you think you need is already in your hands. Start with your thumb on 2, and progress, keeping track of how many fingers you've flipped until you get to 12.

2... 4... 8... 16... 32... 64... 128... 256... 512... 1024... 2048... 4096!

Yes, the correct answer is 4096, not 1024, and you did it with just your fingers. So, if you're ever asked "What's 2^x", where x is some relatively small number that you can get to quickly, you know now to use your fingers. I'll show you an easy way to tackle it if 'x' is relatively large, again, without a calculator, but I'll save that for another post.

Make sure you keep this in mind, however. You never know when you'll be asked.

UPDATE: Some people have had trouble understanding my post, regarding counting binary on your fingers, so let me explain how to do so. First, we need to look at the mathematics of exponentials. Let's start at 2^0. It is defined as 1. What's 2^1? 2. 2^2 = 4, 2^3 = 8, 2^4 = 16, etc. See a pattern. The result of the expression is doubling for every exponent increase by 1.

Now, start counting on hands, starting with your right hand thumb, and continuing through the fingers until we reach the pinky on your left hand (10 fingers). So, you right hand thumb represents 2^1. Your index finger represents 2^2, your middle finger represents 2^3, and so on. So, your left hand pinky will be 2^10. Now, remember the pattern? 2^1 = 2, 2^2 = 4, etc. So, the result of your thumb is 2, your index finger 4, your middle finger 8, your ring finger 16 and your right hand pinky finger 32. See the pattern again? So, continuing, your left hand pinky, making it 2^10, is 1024. We need 2^12, so count two more fingers, and you get 4096.

Easy.

{ 5 } Comments

  1. Orra using Firefox 2.0.0.3 on Ubuntu | May 18, 2007 at 2:18 pm | Permalink

    You had me confused there for a minute. I spend too long trying to understand you :-p. I though you had in mind something like you can do when you multiply by nine.

    I do like counting in binary. Just the other day, somebody said that they could "count the [few] number of times" someone had done something on one hand. I had to point on 31 isn't quite as small as 5. (-:

  2. goalieca using Firefox 2.0.0.3 on Ubuntu 64 bits | May 18, 2007 at 3:38 pm | Permalink

    the way i remember is 2^10 = 1KB = 1024

    2^20 = 1MB = 1024KB
    2^30 = 1GB = 1024MB etc.

    so the easy way is to do

    2^10 * 2^2 = 4-something which i know from memory as 4096

  3. Michael Wheatland using Firefox 2.0.0.3 on Ubuntu | May 18, 2007 at 6:04 pm | Permalink

    I am really sorry. But there are a whole lot of people using Ubuntu and catching up with the planet who have not done a programming course.

    I would love to understand the counting method. Maybe a little more detail about the way you use your fingers and how you derive the number from them would help people understand.

    P.S. Thanks for all of your other insightful blog posts. I really enjoy them.

    Mike From Australia.
    -A non-IT Ubuntu User

  4. Jon using Opera 9.20 on Windows XP | May 21, 2007 at 5:03 am | Permalink

    you are such a genius! please tell me you are still in highschool.

  5. Aaron using Firefox 2.0.0.3 on Ubuntu | May 21, 2007 at 6:22 am | Permalink

    Jon- That's a pretty intelligent comment. Really adds to the conversation at hand. Thanks for stopping by.

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