If you are taking 3 7/8 squares and drawing a line diagonally down the middle and sewing a 1/4" on either side of the drawn line then cutting along the drawn line to get two HST units, you should end up with 3" unfinished HST units and once in the quilt they would measure finished at 2 1/2"
If you are taking a 3 7/8 square and just sewing one seam diagonally down the middle I'm not sure what you get besides a lot of wasted fabric.