Help with binary division problem dividing $1001011010000$ by $1001$

Question

I have this binary division practice problem, I am not sure how to deal with a leading 1 when pulling down the next bit. Here is my process, I'll try to make it clear to where my confusion comes about, I'm not quite sure on how to format the long division symbol here, so please pretend that $1001)....$ is in front of all the bits below and accept my apologies.

I also use the code block as it wasn't clear within a latex block imho.

 1001011010000
-1001
    00       //remainder 0 bring down next bit
    001      //smaller than 1001 bring down next bit
    0011     // still smaller bring down next bit
      110    //still smaller bring down next bit
      1101   //bigger subtract/XOR 1001 
     -1001 
       1000  //bring down next bit, here starts my confusion!

should do this next?:

 10000
-01001

if yes, do I ignore the leading 1? Or how do I proceed, I can't find an example in the textbook we use or elsewhere online and I've looked for a few days.

it's the only example where this occurs but I'm guessing all the other ones were picked to be nicely solvable.

thank you for looking at this for me and helping me understand on how to proceed now.

Answer 1

In the next step, subtract 1001 from 10000, yielding 0111.

You don't just ignore the leading 1 in 10000 -- you need it to borrow from, or the subtraction would be impossible!

Note that just in base ten or any other base, you need to subtract the (multiple of) the divisor from the remainder-so-far. That may require keeping track of borrows. Subtraction is not the same thing as binary XOR even though for some inputs it gives the same results.