Carry-save Adder - The Basic Concept

The Basic Concept

The idea of delaying carry resolution until the end, or saving carries, is due to John von Neumann.

Here is an example of a binary sum:
10111010101011011111000000001101
+ 11011110101011011011111011101111.

Carry-save arithmetic works by abandoning the binary notation while still working to base 2. It computes the sum digit by digit, as
10111010101011011111000000001101
+ 11011110101011011011111011101111
= 21122120202022022122111011102212.

The notation is unconventional but the result is still unambiguous. Moreover, given n adders (here, n=32 full adders), the result can be calculated in a single tick of the clock, since each digit result does not depend on any of the others.

If the adder is required to add two numbers and produce a result, carry-save addition is useless, since the result still has to be converted back into binary and this still means that carries have to propagate from right to left. But in large-integer arithmetic, addition is a very rare operation, and adders are mostly used to accumulate partial sums in a multiplication.