"home" may be conceived as a dwelling, a place, or a state of mind.
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Richard doesn't have a home that marks a sense of place or belonging. The home he shares with his grandmother is marked by defiance. He doesn't embrace her fierce spirituality and doesn't want to be a part of it. Granny slaps him when he doesn't conform, and he usually doesn't. Violence is a symbol and a reality in the "place" he'd call home, but it isn't his home. Later in the novel he'll burn it to the ground.
Richard's true home is found in the world of literature. It's the place he can escape to and no violence can touch him. Racism doesn't exist, being a "black boy" doesn't matter. Reading changes his life; it allows him to feel for the very first time; it is the reason for his first “total emotional response.”
Richard's need to read can be equated with his desire to read. The novel never speaks to his needs outside of this context.