This thesis illustrates the usefulness of the full adder as the elementary cell for designing cellular arrays for arithmetic. It Is shown that basic arithmetic operations, number system conversion, matrix operations and computation of common library functions can be implemented using full adder arrays. It is further shown that fault detection is particularly easy in full adder arrays. The four neighbor full adder array can be tested for the presence of a single faulty cell by applying exactly eight tests, irrespective of the size of the array. The full adder arrays for practical applications turn out to be a little more difficult for fault detection. The number of tests is shown to grow almost linearly with the number of primary input terminals in these arrays. In four neighbor half adder arrays the number of tests grows approximately as the square of the number of primary input terminals.