A programmable cellular array is investigated in this thesis. Each cell in the array is a multi-state network containing combinational logic and a data storage element. The function performed by a cell is determined by the state of the cell and by inputs from neighboring cells. This method of choosing the cell's function allows any combination of cell states in a row or a column. Also, utilization of signals from neighboring cells allows internally generated (as well as external) signals to control a cell. The array is utilized by first programming it to perform several operations and then applying microinstructions which cause the operations to be executed. (A program is a specification of the state of the cells in the array.) The microinstructions contain both data and control information so that all inputs are to the top of the array. This feature reduces the number of external pins to the array. The array can be programmed to operate as an arithmetic processor capable of performing several arithmetic operations. This ability is demonstrated by the implementation of algorithms to perform binary addition, subtraction, multiplication, and division. The array can be programmed to perform other useful operations including conversion between BCD and binary representations, double-precision addition, decimal addition and subtraction, and permutation of variables.