i need help with Binary numbers!

Question

freckles · Answer

What kinda help?

anonymous · Answer

I really dont understand them its all greek to me

freckles · Answer

It is just a base 2 system
0's and 1's

anonymous · Answer

you can ask 10 questions....

anonymous · Answer

i get the base2 part  what i dont get it how to write them as numbers

freckles · Answer

For example
$$10_{10}=1 \cdot 2^3+0 \cdot 2^2+ 1 \cdot2^1+0\cdot 2^0=1010_2$$

anonymous · Answer

im suppose to write 21 in binary i got the answer off google but i still need to understand how to do it for myself

freckles · Answer

Do you understand what I did with write 10 in base 2?

anonymous · Answer

We work in base 10

base = n

so in this case n = 10

from right to left, lets call the right digit 1, then 2, 3 ...

The value of the first digit is equal to the digit * ( 10 ^ (1 - 1)) = digit * 1
so the value of the second digit is equal to the digit * (10^(2-1)) = digit * 10
the third is digit * (10 ^ (3-1)) = digit * 100
...

so in base 2 (binary) the value of the first digit is the digit * (2 ^ (1 - 1)) = digit * 1
second is digit * (2 ^ (2 - 1)) = digit * 2
third: digit * (2 ^ (3-1)) = digit * 4
next is 8, then 16 ...

So if I have the binary number 1010, the value is 1*8 + 0*4 + 1*2 + 0*1 = 10

Do you need help converting the other way?

anonymous · Answer

I really dont understand them its all greek to me

anonymous · Answer

no i think thats clear thank you

anonymous · Answer

OK, start with 21.

Divide by 2 to get 10 remainder 1 <- this remainder is what we want
Then divide 10 by 2 to get 5 remainder 0 <- again what we want
divide 5 by 2 to get 2 remainder 1 <- Yeah again
divide 2 by 2 to get 1 remainder 0 <-
divide 1 by 2 to get 0 remainder 1 <-

Then we rewrite the remainders in reverse order to get 10101

So basically we just keep dividing the whole numbers by two until the whole number is 0. Then the remainders in reverse order will give the binary number

freckles · Answer

or 
      5               2                 1                0
   ---            ---              ---              ---
2| 10          2|  5           2|   2           2 | 1
  -10             -4              - 2               -0
    ---          ---                ---           ----
     0                1                 0                 1

freckles · Answer

lol yeah what he said 
I was still playing with 10 in this example

anonymous · Answer

you guys are awsome