Page 538 - Introduction to Information Optics

9.4. Parallel Signed-Digit Arithmetic

z;« z

Fig. 9.20. Tree structure for the two-step digit-set-restricted MSD addition/subtraction [144]. The
functional block A represents the computation rules generated from Eqs. (9.51) and (9.52) while
the functional block B represents the computation rules generated from Eqs. (9.53) and (9.54).

listed as follows:
z;~ ^ C&, (9.53)
+
z, = S&. (9.54)
Figure 9.20 shows the tree structure for the two-step digit-set-restricted MSD
addition. The functional block A represents the computation rules generated
from Eqs. (9.51) and (9.52), while the functional block B represents the
computation rules generated from Eqs. (9.53) and (9.54). An example showing
the application of the aforementioned technique is illustrated below.

(XI)
(Yl) 001001111 =(53)! o
(U) 000001100
010100011
011000110

step 1: (C) 0010111k/)
(S) 100101111

step 2: (Z~) 001010000
+
(Z ) 100100001
(Z): lOTlTOOOl =(209)i 0

9.4.2.3. Multiplication
Multiplication of two N-digit MSD numbers A a and
- lN- 2
B - lb N_ 2...b 0 generates a 2N -digit product P — P 2N- \P2N~2---Po-