# binary division discrepancy

• Mar 19th 2013, 06:51 PM
fran1942
binary division discrepancy
Hello, I am trying to understand the following modulo 2 long division.
I understand that 1101 goes into 1111, so you write a 1 on the top.
The next stage after 'XOR'ing is to bring down the 1.
Now, 1101 does not go into 101, so you write a 0 at the top. So far so so good.
Now you bring down another 1 and 1101 still does not go into 1011, so how come they wrote a 1 in the third position at the top ? Shouldn't that be a zero ?

If someone could please explain where I am going wrong, I would most grateful.
• Mar 19th 2013, 07:21 PM
Shakarri
Re: binary division discrepancy
It is wrong. In the second part of the division they take 1101 away from 1011 incorrectly.
• Mar 20th 2013, 12:19 AM
fran1942
Re: binary division discrepancy
sorry, I have explained myself more clearly in the edited first post.
Still looking for an answer if anyone can help.
• Mar 20th 2013, 05:49 AM
Shakarri
Re: binary division discrepancy
Ok I thought you just wanted confirmation that it was wrong.

Quote:

so how come they wrote a 1 in the third position at the top ? Shouldn't that be a zero ?
Yes they made a big mistake there.

It should look like this
http://puu.sh/2kPgM
• Mar 20th 2013, 06:50 AM
Soroban
Re: binary division discrepancy

$\text{Hello, fran1942!}$

$\text{The problem is: }\:2026 \div 13 \:=\:155, r11$

Code:

                       1 0 0 1 1 0 1 1               -----------------------       1 1 0 1 | 1 1 1 1 1 1 0 1 0 1 0                 1 1 0 1                 -------                     1 0 1 1 0                       1 1 0 1                     ---------                       1 0 0 1 1                         1 1 0 1                         --------                           1 1 0 0 1                             1 1 0 1                           ---------                             1 1 0 0 0                               1 1 0 1                             ---------                               1 0 1 1
I suspect a typo in the problem.

$\text{If the dividend were }11,\!111,\!101,\!{\color{red}10}\;\!0_2$

. . $\text{the problem would be: }\:2028 \div 13 \:=\:156$