I am searching for information on the following soldier and clarification on what unit he served in. This is what Booth has to say:

Hall, William F., Pvt. Co. C, F, and S.,4th Battn La. Inf. En. Feb 21, 1862, Winnsboro, LA. Present for Duty on rolls to Feb., 1863.

Is this Battalion the same 4th LA Infantry Battalion that Mr. Bergeron states was organized in Richmond, July 10, 1861, and was most likely in Georgia or South Carolina at the time of William's enlistment (see Pg. 157 of his book)? How could William have enlisted in this unit in Winnsboro?

Thank you for your assistance.