You can use axml2xml.pl tool developed a while ago within android-random project. It will generate the textual manifest file (AndroidManifest.xml) from the binary one.
I'm saying "textual" and not "original" because like many reverse-engineering tools this one isn't perfect and the result will not be complete. I presume either it was never feature complete or simply not forward-compatible (with newer binary encoding scheme). Whatever the reason, axml2xml.pl tool will not be able to extract all the attribute values correctly. Such attributes are minSdkVersion, targetSdkVersion and basically all attributes that are referencing resources (like strings, icons, etc.), i.e. only class names (of activities, services, etc.) are extracted correctly.
However, you can still find these missing information by running aapt tool on the original Android app file (.apk):
aapt l -a <someapp.apk>