Adder (electronics) - 3:2 Compressors

3:2 Compressors

We can view a full adder as a 3:2 lossy compressor: it sums three one-bit inputs, and returns the result as a single two-bit number; that is, it maps 8 input values to 4 output values. Thus, for example, a binary input of 101 results in an output of 1+0+1=10 (decimal number '2'). The carry-out represents bit one of the result, while the sum represents bit zero. Likewise, a half adder can be used as a 2:2 lossy compressor, compressing four possible inputs into three possible outputs.

Such compressors can be used to speed up the summation of three or more addends. If the addends are exactly three, the layout is known as the carry-save adder. If the addends are four or more, more than one layer of compressors is necessary and there are various possible design for the circuit: the most common are Dadda and Wallace trees. This kind of circuit is most notably used in multipliers, which is why these circuits are also known as Dadda and Wallace multipliers.