# Not sure how to do binary division

I saw this question in my textbook:

It doesn't look right. From what I understand:

110101 into 101000110100000.

110101 can't go into 101000, so you extend it by one, then do 110101 into 1010001, no? I'm confused and I don't understand how to perform this specific question I link to.

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If it actually were binary long division, it would look like this:

               110001010
┌────────────────
110101 │ 101000110100000
- 110101
────────
111001
- 110101
────────
1000100
- 110101
────────
111100
- 110101
─────────
1110


(Converted to decimal, this means that 20896 ÷ 53 = 394, remainder 14.)

However, your textbook looks like it's actually doing CRC "division" which uses bitwise XOR instead of subtraction. I wish they wouldn't confuse students by calling this operation "division" when it's not.

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Wow, I've been stressing at this for like two hours. Thank you so much, you just saved me for my exam tomorrow, at least for one question. The CRC division is so much easier! –  soju Apr 20 '12 at 4:30
For what it's worth, this operation is division; it's just division in the ring of polynomials $\mathbb{Z}_2[x]$ rather than division over $\mathbb{Z}$. –  Steven Stadnicki Apr 20 '12 at 4:31
True. But it's not the usual division operation, and that point confused me when I was in college, just like it confused soju tonight. –  Dan Apr 20 '12 at 4:34