A system for assembling a framing assembly for a floor or ceiling in a modular construction unit, characterized in that the system comprises: a truss elevator and storage system comprising a truss storage rack, which has a plurality of levels on which trusses can be stored, and a truss elevator configured to raise and transport trusses onto one of the levels of the truss storage rack and/or retrieve and lower trusses from one of the levels of the truss storage rack; a truss placement system configured to receive trusses, via a truss conveyor system of the system, from the truss elevator and storage system, wherein the truss placement system is configured to position trusses on an assembly conveyor, the trusses being spaced apart from each other by a predetermined distance and, optionally, wherein the truss placement system is configured to position the trusses on the assembly conveyor in a sequential manner, the assembly conveyor being configured to advance by a distance corresponding to a pitch between adjacent trusses in the framing assembly before a further truss is positioned by the truss placement system on the assembly conveyor; a joist placement system configured to receive and arrange dimensional lumber that forms joists adjacent lateral edges of the trusses on opposite sides of the assembly conveyor; a framing system comprising the assembly conveyor and a plurality of first fastening devices configured to move along a length of the assembly conveyor to attach the joists to the trusses via applying a plurality of fasteners in at least one predetermined fastener pattern through the joists and one of the trusses; a sheathing/drywall installation system configured to position a plurality of panel members (30, 40) over an exposed surface of the framing assembly after the trusses and the joists are fastened together at the framing system, the panel members (30, 40) being positioned to cover all or a designated portion of the exposed surface of the framing assembly according to a panel placement pattern associated with the framing assembly being assembled; and a fastening system comprising a plurality of second fastening devices to attach, by applying a plurality of fasteners through at least one of the panel members (30, 40) and one of the trusses or the joists of the framing assembly, the panel members (30, 40) to the framing assembly. a truss elevator and storage system comprising a truss storage rack, which has a plurality of levels on which trusses can be stored, and a truss elevator configured to raise and transport trusses onto one of the levels of the truss storage rack and/or retrieve and lower trusses from one of the levels of the truss storage rack; a truss placement system configured to receive trusses, via a truss conveyor system of the system, from the truss elevator and storage system, wherein the truss placement system is configured to position trusses on an assembly conveyor, the trusses being spaced apart from each other by a predetermined distance and, optionally, wherein the truss placement system is configured to position the trusses on the assembly conveyor in a sequential manner, the assembly conveyor being configured to advance by a distance corresponding to a pitch between adjacent trusses in the framing assembly before a further truss is positioned by the truss placement system on the assembly conveyor; a joist placement system configured to receive and arrange dimensional lumber that forms joists adjacent lateral edges of the trusses on opposite sides of the assembly conveyor; a framing system comprising the assembly conveyor and a plurality of first fastening devices configured to move along a length of the assembly conveyor to attach the joists to the trusses via applying a plurality of fasteners in at least one predetermined fastener pattern through the joists and one of the trusses; a sheathing/drywall installation system configured to position a plurality of panel members (30, 40) over an exposed surface of the framing assembly after the trusses and the joists are fastened together at the framing system, the panel members (30, 40) being positioned to cover all or a designated portion of the exposed surface of the framing assembly according to a panel placement pattern associated with the framing assembly being assembled; and a fastening system comprising a plurality of second fastening devices to attach, by applying a plurality of fasteners through at least one of the panel members (30, 40) and one of the trusses or the joists of the framing assembly, the panel members (30, 40) to the framing assembly.