Senbei Norimaki, known as Dr. Slump, is a genius inventor living in Penguin Village. Orphaned in childhood, he developed a dislike for dogs after one insulted his intelligence. He attended Penguin Village Middle School, forming his first romantic attachment to his teacher there. His life transformed dramatically with the creation of Arale Norimaki, an android girl he introduces to villagers as his younger sister or daughter. Arale possesses superhuman strength but requires glasses for nearsightedness. Senbei frequently devises gadgets to manage her behavior or hide her robotic nature, inventions that often trigger chaotic results. A time-travel adventure led Senbei and Arale to discover an egg, which hatched into the winged creature Gatchan, adding another member to their household.

Senbei harbors romantic feelings for Midori Yamabuki, Arale's teacher. After repeated failed attempts to win her affection, he accidentally proposes while she is using the toilet; she accepts, leading to their abrupt marriage. They later have a son, Turbo Norimaki, who displays telekinetic abilities from infancy. Turbo occasionally assists his father, such as secretly repairing the Dragon Radar during Goku's visit when Senbei struggles with its advanced technology.

Senbei's inventions span the practical and the absurd. Notable creations include the See-Thru Glasses (for voyeurism, quickly destroyed), the Big-Small Ray Gun (enlarging or shrinking objects), the Time Slipper (enabling time travel), and the Reality Machine (materializing objects from images). An upgraded Reality Machine 2 later generates items purely through imagination. Many inventions backfire spectacularly, like the Ponpoko Morph Gun causing unintended chaos when misused for transformations.

Within the Dragon Ball narrative, Senbei appears when Goku chases General Blue to Penguin Village. Unable to fix Bulma's Dragon Radar, Turbo covertly handles the repair. Senbei directs Arale to defeat Blue after he threatens Goku. In Dragon Ball Super, Senbei wins the "World Invention Award" for the Reality Machine 2, surpassing Bulma. During the ceremony, the vengeful ghost of Dr. Mashirito possesses Arale and the Gatchans. Senbei aids Bulma in summoning Beerus by using his invention to create a food-based capsule, ultimately leading to Mashirito's defeat.

A recurring trait allows Senbei to transform into a taller, more handsome version of himself when serious, though the effect lasts only three minutes. His personality blends lecherous tendencies with genuine scientific curiosity, often driving him to create inventions for trivial or romantic purposes. Despite his flaws, he demonstrates care for his family, particularly Arale and Turbo.