Digital Arithmetic

Basic Carry-Ripple Adder (CRA) and FA Implementation

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2~

Now, the sum bit is

S13 =X13 ~)Y13 ~)'5'13 = 0

Basic Carry-Ripple Adder (CRA) and FA

Implementation

We review here the carry-ripple adder, which corresponds to the basic (carry-

propagate) addition algorithm. As shown in Figure 2.4, this adder consists of

an array of 1-bit adders

(full-adders

or FAs) defined by expressions (2.4). The

correctness of this adder implementation can be shown by induction, using the

definition

ofci

given by expression (2.6).

Consider now the delay of the addition. Since there is no completion signal,

it is necessary to consider the worst-case ...