109.062510
First convert the whole part 109 to binary this way:
Divide 109 by 2 = 54.5 that ends with .5, so the last digit is 1.
Divide the whole part 54 by 2 = 27, a whole number so 2nd to last digit is 0.
Divide 27 by 2 = 13.5 that ends with .5 so 3rd to last digit is 1
Divide the whole part 13 by 2 = 6.5, that ends with .5 so the 4th to last digit is 1.
Divide the whole part 6 by 2 = 3, a whole number so 5th to last digit is 0
Divide 3 by 2 = 1.5. That ends with .5 so 6th to last digit is 1
Divide the whole part 1 by 2 = 0.5, that ends with .5 so the 7th to last digit is 1.
The whole part is 0, so you're done with converting 109.
10910 = 11011012
Now we convert the fractional part .0625 to binary:
Multiply .0625 by 2 = .125, the whole part is 0, so the 1st radix point is 0.
Multiply .125 by 2 = .25, the whole part is 0, so the 2nd radix point is 0.
Multiply .25 by 2 = .5, the whole part is 0, so the 3rd radix point is 0.
Multiply .5 by 2 = 1, the whole part is 1, so the 4th radix point is 1.
There is no fractional point left over, so we are done, and the fractional
part is .0001
So the conversion of 109.062510 is 1101101.00012
[If there had been a fractional part left over we would have multiplied just
the fractional part by 2, and the next radix point is always the whole part,
which will either be 1 or 0.
Edwin
