binary division $11010 \div 100$?

Question

I'm trying to calculate binary division of $11010 \div 100$.

I got an answer $11.1$ which is wrong? Apparently I need to get $6.5$ (i.e $110.1$) as the answer. Can you anyone tell me how?

Answer 1

Here's what I get from long division:

$$ \require{enclose} \begin{array}{r} 110.1 \\[-3pt] 100 \enclose{longdiv}{11010.0} \\[-3pt] \underline{100}\phantom{00.0} \\[-3pt] 101 \phantom{0.0} \\[-3pt] \underline{101}\phantom{0.0} \\[-3pt] 100 \phantom{.} \\[-3pt] \underline{100}\phantom{.} \end{array} $$

How did you do it?

If you still think it should be done differently, you can click "edit" under my answer to see how I formatted the long division procedure, and then you can "edit" something like that (but altered to show your own steps) into your question.

Alternatively, when I learned long division with decimal numbers, I learned you could save some trouble by discarding zeros at the end of the divisor and shifting the decimal point the same number of places left. For example, to do $92566 \div 400$ it is sufficient to find $925{\color{red}{\mathbf .}}66 \div 4$. This applies equally well in any other base; in your problem, we find that

$$11010 \div 100 = 110{\color{red}{\mathbf .}}10 \div 1, $$

and now you don't need to set up the long division at all.

Answer 2

On any base, if the last digit of the numerator is $0$ and the denominator is $10$, the quotient is the numerator minus that final digit.