A carry-save adder is a type of digital adder, used in computer microarchitecture to compute the sum of three or more n-bit numbers in binary. It differs from other digital adders in that it outputs two numbers of the same dimensions as the inputs, one which is a sequence of partial sum bits and another which is a sequence of carry bits. The carry-save unit consists of n full adders, each of which computes a single sum and carry bit based solely on the corresponding bits of the three input numbers. Given the three n - bit numbers a, b, and c, it produces a partial sum ps and a shift-carry sc:
- <math>ps_i = a_i \oplus b_i \oplus c_i</math>
- <math>sc_i = (a_i \wedge b_i) \vee (a_i \wedge c_i) \vee (b_i \wedge c_i)</math>
The entire sum can then be computed by:
- Shifting the carry sequence sc left by one place.
- Appending a 0 to the front (most significant bit) of the partial sum sequence ps.
- Using a ripple carry adder to add these two together and produce the resulting n + 1-bit value.
When adding together three or more numbers, using a carry-save adder followed by a ripple carry adder is faster than using two ripple carry adders. This is because a ripple carry adder cannot compute a sum bit without waiting for the previous carry bit to be produced, and thus has a delay equal to that of n full adders. A carry-save adder, however, produces all of its output values in parallel, and thus has the same delay as a single full-adder. Thus the total computation time (in units of full-adder delay time) for a carry-save adder plus a ripple carry adder is n + 1, whereas for two ripple carry adders it would be 2n.
