Digital Arithmetic

496 c. >~:~ J:~i, F:~,:~'~i : ~!i~ R~: :~: Digit-Serial Arithmetic

9~

for the 2D vector normalization)

x y

c = s - 9.5

v/.2 +y2 ../,2 +y2

The corresponding timing diagram is given in Figure 9.4(b).

The online delay of the network is the sum of online delays of the operations

on the longest path. For r -- 2, we obtain from Table 9.1

A norm --

81 + 82 + 83 + 84 = 3 + 2 + 4 + 4 = 13

9.6

The total execution time for the composite operation is

D,orm

-- Anorm

-~- 4 + n.

The more levels there are in a sequence of operations and the longer the

precision, the more advantageous is the online approach.

To reduce further ...