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I have an HW question where I found an answer that matches mine, but their breakdown confuses me.

Ques: What is 4365 - 3412 when these values represent unsigned 12-bit octal numbers? The result should be written in octal. I used binary and then looked up the Octal to obtain 753

Found solution: 4365-3412 = 0753 This is because 5-2 = 3 (makes sense), 6-1 = 5 (yep), 8+3-4=7 #we need a carry here, since 3<4 and 4-4=0

I can see where they got 8 (I think) 3+5=8, but why did they do that and how are we getting a carry for the ending of 4-4=0. Appreciate any help/reference.

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  • $\begingroup$ where they got 8 since your base is 8, you have $43_8 = 4 \cdot 8 + 3 = 3 \cdot 8 + (3 + 8)$). I mean, it's the same thing as in base 10: e.g. when computing $53 - 34$, for the last digit you'll compute $10 + 3 - 4 = 9$, and for the first digit: $(5 - 1) - 3 = 1$. How are we getting a carry for the ending of 4-4=0 - it should be $(4-1)-3=3-3=0$. $\endgroup$
    – user114966
    Apr 16, 2021 at 21:09
  • $\begingroup$ (3+5=8 did you start adding result digits? Do you do that using a different representation, say, decimal?) $\endgroup$
    – greybeard
    Apr 17, 2021 at 6:41
  • $\begingroup$ In this context it's called borrow, not carry. $\endgroup$
    – Yuval Filmus
    Apr 19, 2021 at 6:21
  • $\begingroup$ They are using the usual subtraction algorithm. I assume that you know how to subtract numbers in decimal. It is precisely the same algorithm, only in a different base. $\endgroup$
    – Yuval Filmus
    Apr 19, 2021 at 6:21

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Thanks everyone! I believe I came to the right conclusion after the responses: 4365 = 4 x 8^3 + 3 x 8^2 + 6 x 8^1 + 5 x 8^0 2048 + 192 + 48 + 5 = 2293

3412 = 3 X 8^3 + 4 x 8^2 + 1 X 8^1 + 2 X 8^0 1536 + 256 + 8 + 2 = 1802

2293-1802 = 491 or OCT 753

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  • $\begingroup$ I refrain from improving the layout of this answer: I can't believe the purpose of the question was octal to decimal and decimal to octal conversion. $\endgroup$
    – greybeard
    Apr 21, 2021 at 22:09

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