set up some rows and columns thusly...

A B C D
format as general
A B A OR B
3 0 0 FALSE OR(B3="1",C3="1")
4 0 1 FALSE OR(B4="1",C4="1")
5 1 0 FALSE OR(B5="1",C5="1")
6 1 1 FALSE OR(B6="1",C6="1")

format as text
A B A OR B
10 0 0 FALSE OR(B10="1",C10="1")
11 0 1 FALSE OR(B11="1",C11="1")
12 1 0 FALSE OR(B12="1",C12="1")
13 1 1 FALSE OR(B13="1",C13="1")

at the right is the formula used in the column marked 'A OR B'.
first format the entire page as 'general'
then format the lower group of 0's and 1's as 'text'
the result sometimes works.

(yes, I could have used the more straighforward OR(Bx,cx), but this is
simply an example. my actual spreadsheet has a much more complicated
function.)

copy the 0's and 1's from the upper group and do a paste or paste special
value over the top of the lower group.
the formula results all change to FALSE which is WRONG!

why does Excel not preserve the formatting of the cells when pasting?

but if I type the lower group of 0's and 1's in by hand, the formulas work
okay.
I can't type in 4000 lines of data by hand!