He told Hutton: "It has done so through your purposeful, persistent and gross conduct in failing in that most basic and fundamental requirement that is upon every parent, to feed her child adequately."
Hutton was convicted of manslaughter Thursday at Bradford Crown Court.
The judge said the 43-year-old mother of eight had an alcohol problem and that "you placed your own selfish addiction to drink well before your responsibilities to your many children".
The judge said Hamzah's body was only discovered after a rookie police support officer visited the house following complaints from neighbours about dirty diapers being thrown into their yard. The officer became concerned that something was seriously wrong.
Hutton admitted neglecting five of her older children, aged between 5 and 13. The judge said they were found in "appalling conditions of squalor," in a house strewn with pizza boxes, used diapers, vodka bottles and cat faeces - and containing the dead body of their brother.
Hutton's partner Aftab Khan, the father of all eight children, did not live with the family.
Hutton's oldest son, 24-year-old Tariq Khan, was given a two-year suspended sentence for preventing burial of Hamzah's body.
Tariq Khan told police that his mother had threatened to kill her other children and to burn down the house if he went to the authorities.
An inquiry has been called into how the abuse went unnoticed by the authorities for so long.
- AP