Binary ~ Dividing

As with addition and subtraction, I will start out with a table of values and rules that describe how to divide in binary, and then I will do an example problem and explain how it works.

Dividing Values	Rule
1 / 0	Not Possible, Zero has no value(this is true in any base)
0 / 1	0, Nothing can go into 0 more than 0 times.
1 / 1	1

Example:
101101 / 10
Answer: 10110

In order to do dividing in binary, it will require you to know a minimum of 4th grade long division skills. This is because, the only way to really do dividing, without a binary calculator(many scientific calculators do binary, hex, and octal), is to know how to do long division. Also, unlike multiplying, addition, and subtraction, dividing requires you to go from left to right, instead of right to left.

To start this problem, we need to realise that the question is, "How many times does 10 go into 101101, in base 2?" In order to figure that out, we have to find out where our first bit is going to be placed(as in, where the first placeholder is). Looking at 101101, we start with the 1, and ask if 10 goes into it. Obviously, it does not. So, we add on the next bit, 0, and ask again. Does 10 go into 10? It does, and it does so once. So, above the first 0, wew would write 1. Then, we ask if 10 goes into 1, which it doesn't, and then we are dealing with 10 going into 11. It does, with a remainder of 1. Adding that to the next bit, we get 10/10 again, and at the end is a 0, which 10 does not go into. So, we get the answer 10110.

Obviously this problem is very easy, because we are dividing by 10. In binary, 10 = 2, so whenever you are dividing by it, you are taking off a place holder(or in other words, shifting everything to the right one placeholder). This is just like dividing by 10 in base 10, which also moves everything to the right. For example, 50/10 results in 5, 25/10 results in 2.5. But unlike base 10, base 2 has no decimal point. And if you were to actually think of 1/10 in binary, it can be converted to 1/2 in decimal, which gives us .5. So, it's safe to say that 1/10 in binary would be halfway between 1 and 0. And, with rounding you might think this would mean the result is a 1, but it is not. Whenever "rounding" is involved in binary, it always goes down. If you know what sig figs are, it's like that. You'll never end up with an odd number when rounding with .5 in the decimal system, and the same goes in binary.