The BD engine code was used for 1/2 ton trucks from 1942 through 1945 (starting with 1001 at the beginning of the 1942 model year) and were made at the Flint Engine Plant.
Assembled in 1945 would be a good guess, look for the casting date in the right side of the block (sample B145 would be Feb 14, 1945).
There's also serial numbers on the trans and rear that might help nail down year it they are still original.
There's a date code in the top radiator tank as well (B45 = Feb 1945).
Mike B
