A method and apparatus for implementing a discrete cosine transform (DCT) or an inverse DCT (IDCT) with a single hardware unit which applies only positive valued multiplicative coefficients and can be switched to either perform a DCT or an IDCT. The invention processes parallel input digital data signals to produce parallel output digital data signals which represent a discrete transform (either a DCT or an IDCT) of the input data. One aspect of the invention is a method and apparatus for performing discrete transforms using a multiplier which implements MSB-first, bit-serial, carry-save, multiplication of an input word by a positive fixed coefficient. In one class of embodiments, the serially received digits of the input word can take on positive values only. In other embodiments, the serially received digits of the input word can take on positive or negative values. Performance of MSB-first carry-save multiplication allows the design of extremely efficient transforming hardware having low processing delay and high precision, and supporting medium to low speed transform rates. Another aspect of the invention is a method and apparatus for performing discrete transforms using a butterfly addition/subtraction circuit which receives two serial signals and generates both the sum and difference of such signals. In one class of embodiments, the inventive butterfly addition/subtraction circuit implements MSB-first, bit-serial addition and subtraction. In other embodiments, the inventive butterfly addition/subtraction circuit implements LSB-first, bit-serial addition and subtraction.