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Algebra Difficulty 2.0 Junior Find the answer United Kingdom

Ada likes adding numbers! On Monday she added all the three-digit numbers each of whose digits is either $0$ or $1$ . On Tuesday she added all the two-digit numbers each of whose digits is either $2$ or $3$ . On Wednesday she added her answers from Monday and Tuesday. What was the result of Ada’s final addition?

(A) $310$ (B) $421$ (C) $532$ (D) $643$ (E) $754$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.