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.