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U. Glaeser

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Assuming that a single level of the carry lookahead group generates k carry signals simultaneously<br />

with two additional gate delays in the carry path, it can be shown that the total delay of an n-bit CLA is<br />

2 log k n-gate delay units [1]. Theoretically this may be considered one of the fastest adder structures, but<br />

the practical speed of CLA is not necessarily highest because of using complicated gates to implement a<br />

lookahead block in the carry path.<br />

Recurrence solver-based adders are proposed with some popularity to systematically implement CLA<br />

blocks [14–16].<br />

Carry Select Adder<br />

A carry select adder (CSLA) is one of the conditional-sum adder [1,17] that is based on the idea of<br />

selecting the most significant portion of the operands conditionally, depending on a carry-in signal to<br />

the least significant portion. This algorithm yields the theoretically fastest adder of two numbers [18].<br />

In CSLA implementation, two operands are divided into blocks where two sum signals at each bit position<br />

are generated in parallel in order to be selected by the carry-in signal to the blocks. One is a provisional<br />

0<br />

sum si to be selected as a true sum signal si at the ith bit position if the carry-in signal is 0, and the<br />

1<br />

other provisional sum si is selected as a true sum signal if the carry-in signal is 1. This provisional sum<br />

signal pair can be selected immediately after the carry-in signal is fixed.<br />

0 1<br />

In Fig. 9.24 where a 16-bit adder is constructed of CSLA, the provisional carry signal pair ( ci , ci ) is<br />

generated at the highest bit position within each block, in addition to the provisional sum signal pairs<br />

generated at all bit positions within the block. This carry signal pair is used to generate a true carry signal<br />

in a carry-selector block (CS) along with similar signals located at the different blocks. The provisional<br />

sum signals within the block are selected by ci−1 to yield true sum signals si+3:i. Figure 9.25 shows a<br />

combination of RCA and CSLA to construct a 16-bit adder. By such a combination, a high-speed and<br />

small size adder can be realized efficiently [19–21].<br />

c-1<br />

0<br />

1<br />

0<br />

c3<br />

1<br />

c3<br />

a3:0 b3:0<br />

CSLA<br />

CSLA<br />

a3:0 b3:0<br />

FIGURE 9.24 4-bit carry select adder.<br />

© 2002 by CRC Press LLC<br />

0<br />

c3<br />

MPX<br />

1<br />

c3<br />

cs<br />

0<br />

1<br />

s3:0<br />

1<br />

c3<br />

0<br />

c3<br />

1<br />

c7<br />

a7:4 b7:4<br />

CSLA<br />

CSLA<br />

a7:4 b7:4<br />

c-1<br />

1<br />

c7<br />

0<br />

c7<br />

0<br />

c7<br />

MPX<br />

1<br />

c7<br />

0<br />

s7:4<br />

a11:8 b11:8<br />

CSLA<br />

CSLA<br />

a11:8 b11:8<br />

0<br />

c11<br />

MUX<br />

0<br />

s11:8<br />

a15:12 b15:12<br />

CSLA<br />

CSLA<br />

a15:12 b15:12<br />

0<br />

c15<br />

MUX<br />

c3 c7 c11<br />

1<br />

1<br />

c11 1<br />

1<br />

c15<br />

cs<br />

0<br />

c11<br />

1<br />

c15<br />

1<br />

c7<br />

0<br />

c3<br />

1<br />

c11<br />

c-1<br />

c3 1<br />

1<br />

c7 1<br />

c11 0<br />

c11<br />

cs<br />

s15:12

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