Page 550 - Introduction to Information Optics

9.4. Parallel Signed-Digit Arithmetic

Numerator (X) Denominator (Y)
Set initial value, X 0 = X Set initial value, Y 0 = Y

Generate multiplication factors
m,= 2- Y

Multiply X A by m t Multiply Y tby m i

Fig. 9.23. A block diagram for TSD division [154].

for addition. In the receding (addition) step of both schemes, the minterms for
generating the outputs 1 and 2(1,2, and 3) are the exact complement of those
used for generating the outputs I and 2 (T, 2, and 3). Consequently, the former
required 19 (33) minterms for the outputs 1 and 2 (1, 2, and 3) in receding
(addition), as shown in Table 9.31, while the latter required 19 (32) min-
terms for the outputs 1 and 2 (1, 2, and 3) in recoding (addition) as shown in
Table 9.32.

Table 9.31
Reduced Truth Table for QSD Recoding [156] where the Minterms for the T and 2 Outputs
are Digit-by-Digit Complement of that Generating the 1 and 2 Outputs, Respectively

Output literal Minterms
d 3 ,223 d 5l23d d 3l 3dd 222dj T oi2j 22d Toi2J d 2d T(,,dd

d 3l 22d 2T oi23 ^Ji _
d 523dd d 2223d d, 2223 0223 023d 03dd