APL (Dyalog Extended), 11 8 bytes

∊⍕¨'0'=⎕

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Explanation

∊⍕¨'0'=⎕
   '0'=⎕        For each character: 1 if it's '0', 0 otherwise
 ⍕¨             Convert each to string
∊               Flatten into a single string

APL (Dyalog Extended), 11 8 bytes

∊⍕¨'0'=⎕

Try it online!

-3 thanks to @Adám

Explanation

∊⍕¨'0'=⎕
   '0'=⎕        For each character: 1 if it's '0', 0 otherwise
 ⍕¨             Convert each to string
∊               Flatten into a single string

APL (Dyalog Extended), 11 bytes

∊⍕¨~2|⎕UCS⎕

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Port of Riley's 05AB1E answer. This can probably be improved.

Explanation

∊⍕¨~2|⎕UCS⎕
      ⎕UCS⎕     Unicode codepoints of the input
   ~2|          Not mod 2 (i.e. 1 if odd, 0 if even)
 ⍕¨             Convert each to string
∊               Flatten into a single string

APL (Dyalog Extended), 11 8 bytes

∊⍕¨'0'=⎕

Try it online!

Explanation

∊⍕¨'0'=⎕
   '0'=⎕        For each character: 1 if it's '0', 0 otherwise
 ⍕¨             Convert each to string
∊               Flatten into a single string