Discussion
Without a common intermediate representation, how many separate translators would 4 source languages and 5 target machines require?
Answer: B
Correct answer: 20
Without a shared intermediate form every language-machine pair needs its own translator:
\[ 4 \times 5 = 20 \]
against the 9 that a common representation requires. The contrast between \( m \times n \) and \( m + n \) is the point, and it widens rapidly: ten languages and ten machines would need 100 translators against 20 components. It is also why retargeting means rewriting only a back end.
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