Leaving Math::BigInt out of it, you can't have a scalar have a value like "0xdeadbeef" and have perl treat it as the number 0xdeadbeef; the "0x" header is noticed by the perl compiler when compiling a constant, and by things like Math::BigInt::new that explicitly do so, but when perl numifies a string variable, it only looks for decimal numbers. So "0xfoo" will only have the "0" part recognized as a number.

Is there a reason you can't say $predefbi = new Math::BigInt $firststr;?