A data processing apparatus for performing decimal arithmetic operation with the aid of a decimal arithmetic unit having an operation width corresponding to a plurality of bytes. Length value of an operand which is to undergo arithmetic operation of the decimal arithmetic unit is held in an operand length register, while a byte position which constitutes the least significant position in the arithmetic operation is held in an operand point register. An overflow detection controlling circuit generates a control signal in accordance with the contents in both the registers. An overflow detecting circuit detects presence or absence of an overflow by checking a particular byte contained in the output of the decimal arithmetic unit, the particular byte being designated by the control signal produced from the overflow detection controlling circuit.