Abarim Publications' online Biblical Hebrew Dictionary
There are two roots of the form חוץ (hws) but they don't seem to have much to do with each other.
The meaning of the unused root חוץ (hws) is unknown. In the Bible two derivatives occur, both having to do with outside.
The masculine noun חוץ (hus) means the outside. It may describe the outside of a tent or camp (Deuteronomy 23:13) or that of a house of chamber (Judges 19:25, 2 Samuel 13:18), or a city (Numbers 35:4). And it may even describe the outside of a country and mean abroad (2 Kings 4:3), or the outside of a family and mean a stranger (Deuteronomy 25:5). It may also indicate existence without someone (Ecclesiastes 2:25).
Our word may specifically denote that which is outside the houses of a town, namely a street (Isaiah 51:23, 2 Samuel 1:20, 1 Kings 20:34). Jeremiah even received his daily bread from Baker Street (Jeremiah 37:21). But our word may also specifically denote that which is outside enclosed cities, namely the open country (Job 18:17, Psalm 144:13).
A second derivative of our root is the adjective חיצון (hison), meaning outer, such as the outer gate (Ezekiel 44:1), the outer court (Ezekiel 10:5), or the outer wall (2 Chronicles 33:14). It may denote the outer areas of a building (Nehemiah 11:16) and even secondary business of priests (1 Chronicles 26:29).
Scholars insist that the sole occurrence of the word חיץ (hayis) comes from the whole other root חוץ (hws). It means party-wall, which is a thin wall that separate two groups of people and is used only once: in Ezekiel 13:10.