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What Are Binary Numbers? Part 2

How can you guess a secret number between 1 and 1,000 in no more than 10 tries? Why do smart phones come with 16, 32, or 64 GB of storage? And what do both of these questions have to do with binary numbers? Keep on reading to find out!

By
Jason Marshall, PhD,
February 15, 2013
Episode #142

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What Are Binary Numbers? Part 2

Is it possible to always be able to guess a secret number between 1 and 1,000 in no more than 10 tries? Why do smart phones come with 16, 32, 64 or some other strange number of gigabytes of storage? What do both of these questions have to do with binary numbers? In part 1 of this series on binary number basics, we learned what binary numbers are and how you can represent a decimal number (the kind that you’re used to) in binary form. Now that we’re all up to speed on the nuts and bolts of binary numbers, this week we’re going to have a bit of fun using them to solve brain teasers.

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Recap: What Are Binary Numbers?

As we learned last time, the binary system is the simplest number system possible. In contrast to the decimal system’s ten symbols (0 through 9), the binary system uses only two (0 and 1). In the binary system we start counting at 0, then continue to 1, and then—since we’re all out of new symbols—we add a digit to make the binary number ‘10’ representing the number made of one 2 and zero 1s…aka 2. After ‘10’ is ’11’ (or 3), then ‘100’ (or 4), then ‘101’ (or 5), ‘110’ (or 6), ‘111’ (or 7), and so on. 

Each binary digit represents the next higher power of 2. So the far right digit represent 2^0=1, the next represents 2^1=2, then 2^2=4, and so on. All you have to do to figure out the decimal equivalent of a binary number is add up all the powers of 2 that have a ‘1’ in their place. For example, since the binary number ‘1010’ has ‘1’s in the 4th digit (representing 2^3=8) and the 2nd digit (representing 2^1=2), it’s equivalent to the decimal number 8 + 2 = 10.

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