Why did it take me so long to find this? Probably because I didn’t use radix in my Google search. Of course. Thanks to “Philip M” for the clue and thanks to W3Schools.com for the reference (see here for more on the unary “+” operator to convert a string to number).

var str = '37';
var num = (+str);
document.write(num.toString(2));

Should output “100101″.