pulling values from a column and reordering them in another column without spaces

Hi,

I have a couple of columns that look like this in basic form:

Column A Column B
A 1
B 1
C 0
D 2
E 1
F 0
G 2

What I want is in a separate worksheet for it to pull the names (A, B, E) that have 1s next to them in column B and put them in a list.

I could do this kinda manually, but how can I create a nice list in a separate column on a separate worksheet just of the names (column A values) where there is a 1 in column B? All I can think to do is vlookup the data and put blanks where its not equal to 1 and then manually delete out the other rows.

Thanks a lot for the help