Are either top or bottom plates required to be 1 continuous piece of lumber? If it's not required, what is the best way to attach the separate sections; a lapping piece over the top of the joint?
Negative. Bottom plates rarely are in any case, since they're fully supported, though better carpenters tend to splice them on studs.
Simply fasten them to the floor with construction adhesive and/or mechanical fasteners as appropriate. No scab is necessary (though one could help keep things in alignment if not splicing under a stud).
Is the idea here that toe-nailing will help hold the pieces together when the joint is under a stud? Apr 2, 2018 at 17:14
1Right, but if you build your walls on the floor there's no toenailing anyway. Apr 2, 2018 at 17:45
What about the top plate? IBC 2015, 2308.5.4 requires solid blocking not less than 16 inches in length at "joints." Don't "joints" include splices where two top plates touch at their ends?– pophamOct 24, 2018 at 0:18