whenever we start working on Discrete Cosine Transform(DCT), Loeffler algorithm a key role. Furthur if we approach hardware implementation of this algorithm, we find methods based on Distributed Arithmetic and Shift-and-Add. Both of these method stress on multiplierless circuits. In both cases multiplication is either performed by shift and adding or using a ROM which stores the look-up tables.

The point I am asking here is why everyone is neglecting multipliers replacing them by adders,shift registers in circuits. We can make a N-bit multiplier using adders and registers. Can someone highlight the negative impact of using multipliers?

  • $\begingroup$ This is done because such solutions are less demanding in silicon area or time for calculation. the use of short DCT make the coefficient simple and calculation of DCT by combined butterflies more effective in direct form. $\endgroup$
    – Moti
    Dec 4, 2015 at 21:56

1 Answer 1


Once upon a time, chips (processor ICs) did not have anywhere close to millions (now billions) of transistors on them.

A typical fast multiplier, say made out of a tree of layers of carry-save-adder cells, requires a lot more logic gates (thus transistors) than a simple adder, thus also requiring a lot more power, and with less of them fitting on a particular silicon die area.

Repeated conditional-add-and-shift is slower (in the same transistor technology) but requires a lot less logic gates (thus less transistors) when done sequentially.

If an (ancient) FPGA has tons of small memories (but no multipliers), the memories might be useful as look-up tables that are faster than the equivalent logic equations implemented in fabric connected LUT cells.


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