Question 1190037
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I'll do the second example, showing two different ways.<br>
Place values, base 10:
      1 = 10^0
     10 = 10^1
    100 = 10^2
   1000 = 10^3
  10000 = 10^4
   etc.<br>
Place values, base 2:
           1(base 2) =   1 = 2^0
          10(base 2) =   2 = 2^1
         100(base 2) =   4 = 2^2
        1000(base 2) =   8 = 2^3
       10000(base 2) =  16 = 2^4
      100000(base 2) =  32 = 2^5
     1000000(base 2) =  64 = 2^6
    10000000(base 2) = 128 = 2^7
   100000000(base 2) = 256 = 2^8
   etc.<br>
You should understand how to convert from base 10 to base 2 using place values, because it helps you understand numbers in different bases.  But it is a slow and inefficient process.<br>
Here is how to convert 210 (base 10) to base 2 using place values.<br>
The largest power of 2 less than 210 is 128, which is 10000000 (base 2); the number that remains is 210-128=82
The largest power of 2 less than 82 is 64, which is 1000000 (base 2); the partially converted number is 10000000+1000000 = 11000000; the number that remains is 82-64=18
The largest power of 2 less than 18 is 16, which is 10000 (base 2); the partially converted number is 11000000 + 10000 = 11010000; the number that remains is 18-16=2
2 is 10 in base 2<br>
The conversion is 210 (base 10) = 11010000+10 = 11010010 (base 2).<br>
The process involves repeated subtraction and then repeated referral to a list of powers of 2; that makes the process slow.<br>
Here is a far more efficient way to perform the same conversion.<br>
210/2 = 105 remainder 0
105 = 52 remainder 1
52 = 26 remainder 0
26 = 13 remainder 0
13 = 6 remainder 1
6 = 3 remainder 0
3 = 1 remainder 1
1 = 0 remainder 1<br>
The converted number in base 2 is the remainders, written in reverse order: 11010010.<br>
That is a much more efficient process.<br>