Dividing in Base 2 numbers.?

Question

Can anyone help me understand how to divide in base 2 numbers. For instance,

1011/11 in base 2

Answer 1

Most people use a base 10 system. Whatever you use, the base is that "Unreachable" number. For example, in base 10, there is no digit for 10, you start a new column representing how many 10's you've amassed. You have a 1's column a 10's column a 100's column and so forth. To get the numerical value you multiply (most people are so used to it, they just do it in their head). If the number is 823 you can express it as 3X1 plus 2X10 plus 8X100
3x1 = 1
2x10 = 20
8X100=800
-----------------
1+20+800= 821

So 3 plus 20 plus 800. Make sense?

In binary "2" is the unreachable number, so you go 1, 10, 11, 100, etc. You have a 1's, 2's, 4's, 8's column.
The number 11011 would be 1Xone, plus 1xtwo, plus 0Xfour, plus 1xeight, plus 1x16 or 27 in base 10.

1x 1 = 1
1x 2 = 2
0x 4 = 0
1x 8 = 8
1x16 = 16
---------------
1+2+8+16=27

Let's look at your specific numbers 1011, that's

1 x 1 = 1
1 x 2 = 2
0 x 4 = 0
1 x 8 = 8
--------------------
1+2+0+8= 11

Your top number is 11 (in base 10)
Your bottom number:

1 x 1 = 1
1 x 2 = 2
----------------
1+2=3

So the problem states 11/3, that's pretty easy. 3.666(repeating)

With practice, it becomes easier. You learn to recognize the column values and mulitply in your head.

Hope that helps,
Odd

Answer 2

Just like base 10 long division only easier becasue you only have to figure out if the dividend is larger than the divisor to get the next partial quotient (which is a 1 or 0 depending on whether or not the dividend is equal or larger than the divisor)
11 goes into 101 so write down 1 calculate 101-11= 010
Add the 1 from the original dividend to get 0101
11 goes into 0101 so write down another 1 and subtract
0101-11 to get 010 again. This is the remainder and the quotient is 11. So 1011/11 = 11 R 10 which is the same as 11/3 = 3 R 2.

If you want some *serious* fun sometime, figure out how to divide using Roman Numerals ☺


Doug

Answer 3

Base 2 Division

Answer 4

the brief answer is 'no' the closest component you have are 'Factorials' written as n! that are the particular case of 1x2x3x...(n-one million)xn For you case you have pulled out 9! = 362880 as an occasion besides. yet of course there are going to be smaller numbers that are going to be divisible by utilising each and all the numbers interior the series considering (for the example you provide): 9 - would nicely be got rid of considering we've 3 and six already and if a sort has 3 two times (3 and 2x3) as a component then that is going to likely be divisible by utilising 9 8 - we've 4 and six 2 - we can use 4 or 6 so 3x4x5x6x7 = 2520 is likewise divisible by utilising all 9 numbers greater advantageous as much because it (plus 10 of course in actuality). word 840 (as pronounced by utilising previous answerer) isn't divisible by utilising all 9 factors because it is not divisible by utilising 9. although - your fact that they are rarer than primes won't be genuine. It only relies upon no count number in case you're staring at massive numbers or small numbers. each and every 2520 numbers there'll be a sort divisible by utilising one million,2,3..., 9, 10 yet as numbers get bigger top numbers grow to be very uncommon and the kind of top numbers

Answer 5

I guess long division works just as well, as long as you remember you're doing it in base 2. So 11 doesn't go into 10, but it does go into 101 (once...it's either once or not at all). Similarly for subtraction; borrowing works if you remember that 10-1=1.

Answer 6

I would have to convert to base 10 and get 11/3. If this were a whold number i could convert back