How to replace one symbol with two on Turing machine's tape
The way I'd do it is as follows:
The syntax is from the Turing simulator I link to below. It is

[transition name],[symbol]
[next transition],[new symbol],[direction]


The actual code:

name: Binary to Unary
init: moveright2
accept: end

moveright2,_
moveright1,_,&gt;

moveright2,0
moveright2,0,&gt;

moveright2,1
moveright2,1,&gt;

moveright1,_
moveleft,1,&lt;

moveright1,0
moveright1,0,&gt;

moveright1,1
moveright1,1,&gt;

moveleft,_
sub1,_,&lt;

moveleft,0
moveleft,0,&lt;

moveleft,1
moveleft,1,&lt;

sub1,0
sub1,1,&lt;

sub1,1
moveright2,0,&gt;

sub1,_
blankout2,_,&gt;

blankout2,_
blankout1,_,&gt;

blankout2,1
blankout2,_,&gt;

blankout1,1
end,_,&gt;


Basically move till you've passed two blanks(Step 1), then write a 1(Step 2), move left till you find a blank(Step 3), treat the number to the left as a binary number and subtract one from it(see below for details on how this works)(Step 4), Then repeat steps 1-4 until you can't subtract any more(in my case the subtract routine turns all 0's in the number we've been subtracting from to 1 and then hits a blank), go back turning all ones to blanks till you hit a blank, then go one farther turning that one into a blank.

It turns 101 into 11111

Subtraction routine, start at the far right of the number, if it's 0 change it to one and move left doing the same thing to each digit you come across, if it's one see step 1