Page 495 - DSP Integrated Circuits

480 Chapter 11 Processing Elements

The partial products for a 4x4 multiplication (W^ = 4 bits) are shown in Figure
11.11. Notice that some slight variations in the way the partial products are
formed occur in the literature. From the preceding expression and Figure 11.11
the logic realization of the Baugh—Wooley's multiplier can easily be identified.

Figure 11.11 Partial products for a 4x4 Baugh-Wooley's multiplier

A logic realization of the 4x4 array multiplier is shown in Figure 11.12. All bit-
products are generated in parallel and collected through an array of full-adders
and a final RCA. The first term (2) is taken into account by adding a 1 in the stage
(po) that corresponds to the sign-bit. However, if the number range is reduced by
not allowing the number 1, the multiplier can be simplified by removing the last
stage (pi) and PQ is used as the sign-bit. Also the first level of full-adders can be
simplified to half-adders. Notice that the multiplier has a regular structure that

Figure 11.12 Baugh-Wooley's multiplier