You may want to send for his social security application which should have both parents' names.
In the 1920 census in Ashe county NC Pearl Tedder 15 is with her parents in Horse Creek, Londa R and Rosa C Ham, along with Bynom R Tedder one month old, making him born about Dec 1919.
Altho I could not find much on the 1910 census, I noticed many pages are very hard to read. In 1900 Ashe county NC, Horse Creek there is a Tedder family, indexed as Joseph, but the actual handwriting is hard to read. He is 37 NC, wife Lucinda 36 NC, william 16, Adam 14, Matilda 7, George, BYNOM 5, John 1, all b. NC. I could not find more on the family for certain. Nor could I find them on the NC death index for certain. It seems like this Bynom is a good candidate for the father of Bina. But you would want more positive documentation, such as death records, marriage records, etc.