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I need to add the following numbers. I keep getting a result of 10010.101, but the answer is 10100.101. Can anyone confirm that

10100.101

is the correct answer, and that I'm the one mistaken?

Numbers that need to be added:

   1011
  10110
 101100
1011000
Eric Wofsey
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alcatraz
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1 Answers1

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Were the number base $10$, the sum would be $1123221$. We replace the rightmost $2$ by $0$ and carry $1$ to the left: $1123\color{green}{30}1$. Now $3$ becomes $1$ and we carry $1$ to the left: $112\color{green}{41}01$. $4$ becomes $0$, but this time we carry $2$ to the left: $11\color{green}{40}101$. Once again, $1\color{green}{30}0101$. Then $\color{green}{21}00101$. And finally $\color{green}{10}100101$.

  • The first sentence should probably say instead that you start by adding without carrying. Then you take care of the carrying afterward. Then the argument is general and works for arithmetic in any base. See exploding dots: https://www.explodingdots.org/ – Ethan Bolker Oct 27 '18 at 17:21
  • Perhaps I was unclear. Just add columns without carrying with no base in mind. You get a sequence of integers, one per column. Now knowing the base you can "carry" to reduce the integer in each column so as to use a single digit in that base. The underlying principle is that there's no need other than convention/convenience to restrict the "digits" in positional notation. Requiring digits less than the base is just the standard form. So "eleventy one", i.e. $(11)1$ is a nice :two column representation of the base ten $111$. Kids find that fun and enlightening. – Ethan Bolker Oct 27 '18 at 17:33