Reg Ex for even number of 0s and 1s

Question

I am trying to create a regular expression that determines if a string (of any length) matches a regex pattern such that the number of 0s in the string is even, and the number of 1s in the string is even. Can anyone help me determine a regex statement that I could try and use to check the string for this pattern?

Answer 1

So completely reformulated my answer to reflect all the changes:

This regex would match all strings with only zeros and ones and only equal amounts of those

^(?=1*(?:01*01*)*$)(?=0*(?:10*10*)*$).*$

See it here on Regexr

I am working here with positive lookahead assertions. The big advantage here of a lookahead assertion is, that it checks the complete string, but without matching it, so both lookaheads start to check the string from the start, but for different assertions.

1. (?=1*(?:01*01*)*$) does check for an equal amount of 0 (including 0)

2. (?=0*(?:10*10*)*$) does check for an equal amount of 1 (including 0)

3. .* does then actually match the string

Those lookaheads checks:

(?=
    1*    # match 0 or more 1
    (?:   # open a non capturing group
        0     # match one 0
        1*    # match 0 or more 1
        0     # match one 0
        1*    # match 0 or more 1
    )
    *     # repeat this pattern at least once
    $     # till the end of the string
)

Answer 2

So, I have come up with a solution to the problem:

(11+00+(10+01)(11+00)\*(10+01))\*