Clearly, dividing by two in a binary number shifts the decimal point like this:
BaseForm[InputForm[7], 2]
BaseForm[InputForm[7/2 // N], 2]
It gives: 2^^111 and 2^^11.1
Now, why does this not give a similar result?
BaseForm[InputForm[
1 + (1*$MachineEpsilon + 2*$MachineEpsilon + 4*$MachineEpsilon)/
1], 2]
BaseForm[InputForm[
1 + (1*$MachineEpsilon + 2*$MachineEpsilon + 4*$MachineEpsilon)/2],
2]
The only difference here is that the second line has a division by $2$.
2^^1.0000000000000000000000000000000000000000000000000111
and
2^^1.00000000000000000000000000000000000000000000000001
Can anyone explain this last result? I would expect 2^^1.000000000000000000000000000000000000000000000000011