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KEY TO PAGES 141-144
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Adders:Carry Look-Ahead Adder.
Carry Look-Ahead Adder As previously stated, the carry, c i +1, produced at the i -th position is calculated as c i +1 = x i · y i ∨ c i ·( x i ⊕ y i ). This means that a carry is generated if both x i and y i are 1, or an incoming carry is propagated if one of x i and y i is 1 and the other is 0. Therefore, letting g i denote x i y i , we have c i +1 = g i ∨ c i p i , where p i = x i ⊕ y i . Here, g i is the formula for the carry generation condition at the i -th position, i.e., when g i is 1, a carry is generated at this position. Substituting g i –1 ∨ p i –1 c i –1 for c i , we get A carry look-ahead adder can be realized according to this expression, as illustrated in Figure 41.10 for the case of four bits [21]. According to this expression, c i +1’s are calculated at all positions in parallel. It is hard to realize an n -bit carry look-ahead adder precisely according to this expression, unless n is small, because maximum fan-in and fan-out restriction is violated at higher...
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