Digital Arithmetic

76 e ~ A pT E R 2 Two-Operand Addition

Now we define a section ofp groups and determine with a CLG the carry-out

of each group in the section. That is,

c ~1) = Go +

Aoco

C (2) =

G1 + A1Go + A1Aoco

,,.

c (t') -- GI,_I + At,-1Gp-z + "'" + (Ap-iAp-2"-" Ao)co

2.47

Once the carries out of the groups are produced, these carries are used by the

first-level CLA modules to produce the bit carries and the sums. Figure 2.15

shows a 32-bit adder with two-level lookahead (with p = m = 4).

Note that the CLA module is used twice: first to compute A and G (which are

independent of the carry-in to the group) and then, ...