So, the Monk's Martial Arts say:
You can roll a d4 in place of the normal damage of your unarmed strike or monk weapon. This die changes as you gain monk levels, as shown in the Martial Arts column of the Monk table.
Meanwhile, the Tavern Brawler feat says:
Your unarmed strike uses a d4 for damage.
My question is, could either a Monk or a Tavern Brawler choose to deal the flat 1 damage an untrained unarmed strike would do, instead of the d4 or better die?