Is Bill Gates the son of a wood-cutter?

A picture of Bill Gates and his daughter in a restaurant is going viral with a short story.

The story is an exchange between a waiter and Bill Gates. Bill Gates tips $5 after his meal. The dissatisfied waiter said that his daughter tipped him $500 and he questioned why one of the wealthiest man doesn’t tip more. Gates answered that she is the daughter of a Billionaire, on the other hand he is a son of a wood-cutter.

There is no source to confirm if the conversation occurred although on looking into Bill Gates’ lineage, it was found that his father, William H Gates was a prominent lawyer who is now retired. He is also the co-chair of the Bill and Melinda Gates Foundation. Therefore, proving that Bill Gates is not the son of a wood-cutter.