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Here's my code:

let padded = "03";
ascii = `u00${padded}`;

However, I receive Bad character escape sequence from Babel. I'm trying to end up with:

u0003

in the ascii variable. What am I doing wrong?

EDIT:

Ended up with ascii = (eval('"\u00' + padded + '"'));

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What am I doing wrong?

A unicode escape sequence is basically atomic. You cannot really build one dynamically. Template literals basically perform string concatenation, so your code is equivalent to

'0' + padded

It should be obvious now why you get that error. If you want to get the corresponding unicode character you can instead use String.fromCodePoint or String.fromCharCode:

String.fromCodePoint(3)

If you want a string that literally contains the character sequence u0003, then you just need to escape the escape character to produce a literal backslash:

`\u00${padded}`

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