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Write the decimal number 116 in binary.

Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014. Reprinted by permission of Pearson Education Inc., New York.
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Giancoli 7th Edition, Chapter 17, Problem 59


Chapter 17, Problem 59 is solved.

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Transcript for this Giancoli solution

This is Giancoli Answers with Mr. Dychko. So we're going to represent the decimal number 116 using binary. And the answer is 1110100. But the way you get the answer is each binary digit has a certain place value and the first one is two to the power of zero. If this binary digit was a one it would equal two the power of zero which is one. And this next digit is two to the power of one. And so if you had a one here that would give you the binary or the decimal number quantity two. This digit here is two to the power of two, so it's decimal quantity is four. And then this is two to the power of three, decimal quantity eight and so on and so on, two to the power four makes 16 and five makes 32 and two to the power six makes 64. So to figure out how to write a 116 decimal as a binary you take the largest binary digit. And that's still less than a 116. And start with that and then add more as needed until you get this quantity. So if we had two to the power of seven that would be the next binary digit that would be 128. And that doesn't work because 128 is more than 116 so we know that we have to have two do the power of six represented. So two to the powers six makes 64 and then we'll keep adding more and more each subsequent binary digit, we'll make it a one. So long as we don't exceed a 116. So the next one is two to the power five which makes 32 and this total is 96. So that's still not enough. So add another 16 by taking the next binary digit two to the power of four and that makes 112 but that's not enough. So we need to add another four. And so we'll skip this one and we'll add this for a quantity of four to make a total of 116 and everything else would be zero. So this one's a zero, this one's a zero, that one's a zero.