Sorry, but what's a "reading"? I'm not up on legislative lingo.
In Texas, the Constitution requires a bill to be read on three separate days in each House (this can be overridden on a 4/5 vote). Bills are also required to be considered in committee.
Congress uses the same procedure, but it is in their rules, and not required by the US Constitution (or at least I couldn't find it).
The idea is that a bill can't be rushed through on one day when some members might be absent, and also gives them the chance to reconsider.
The basic process (simple version) is this:
(1) Bill is filed in one house or the other (in Texas, identical or similar bills are usually filed in both houses).
(2) Bill is given first reading. This is very perfunctory, and there is usually unanimous consent to dispense with reading the entire bill. So the reading clerk simply reads "HB 31415 by Doe", "HB 31416 by Smith", etc.
(3) The bill is assigned to a committee (or committees) by the presiding officer (speaker in the House, Lt.Governor in the Senate).
(4) The committee hears testimony (this is referred to as hearing). Often they simply postpone further action, effectively killing the bill. Often they will make a substitute for the bill, which is done because there were some technical or other problems found with the bill. If the committee likes the bill, or at least wants it considered by the full house, they report it back to the house.
(5) Bill is given second reading. This is usually the main debate on the bill. Amendments can be offered. Sometimes a bill is sent back to committee. Sometimes the bill passes. Sometimes it fails. Ordinarily a bill that would likely fail would never get this far, unless it was being done to politically embarrass its supporters.
(6) Bill is given third reading. If the bill is uncontroversial, the rules might be suspended to permit immediate consideration (same day) 3rd reading. If it passes on 3rd reading it is final passage by the house, and is then sent to the other house where the procedure is repeated.
Sometimes, a bill might pass on 2nd reading, but fail on 3rd reading, if opponents have talked someone into changing their vote, or possibly because some absent members show up the next day.
In IL there are similarly three readings of each bill in each chamber. Readings only include the reading of the title of the bill.
The first reading is perfunctory. The chamber is generally not in session and the reading is handled by the Clerk. The bill is sent to the Rules committee.
The Rules committee refers the bill to a committee for hearing and recommendation. Bills that receive a favorable recommendation from the committee return to the full chamber and are placed on a calendar of second reading.
After a bill is assigned to committee each step only proceeds with the consent of the sponsor of the bill.
Bills can only be amended in committee or on second reading. Bill are often held on second if negotiations towards an amendment are underway. Amendments on the floor are debatable, but rarely does this occur. The actual second reading is not debated, but allows the bill to move from second to third reading on a non-recorded voice vote.
Debate occurs on the third reading. The final vote is always recorded.