Page 544 - Introduction to Information Optics

9.4. Parallel Signed-Digit Arithmetic 529

Table 9.25
Example of the Quotient-Selected MSD Division, [145] where
X = (0.101lI01) MSD = (0.6640625),,, and D = (0.1110lTl) MSD = (0.8359375) 10
Iteration Partial remainder Quotient digit Quotient word
! w 0 = 0.101 1101 q l = 1 G, = 0.1
2 Wj = 2w 0 -D = 0.1000001 92 == 1 Q? = 0.11
3 w, = 2w, -D = 0.0010101 93 = 0 63 = 0.110
4 w ; = 2w 2 = o.oioiolo 94 = 0 = 0.1100
5 vv 4 = 2w-, = o.ioioToo 9s 1 Q 4
O s = 0.11001
6 w 5 — 2vv 4 - D = o.ioTTiiT 9<, = 1 Ge = 0.110011
7 w = 2w 5 - D = O.OOlOOOT 97 = 0 67 = 0.1100110
8 w 7 = 2w 6 = o.oToooTo

quotient digits, one can use three minterms 10d, 1 Id 01, and Old 0 i for output 1,
and three minterms IQd, Ild 0i, and Oyd 01 for output I.
If we use dual-rail spatial encoding S*S** to encode an MSD digit, the
quotient-digit selection can be done by binary logic operations. The code
used here is S*S** = 01 for 1,S*S**=00 for 0, and S*S** = 10 for I.
Therefore, a quotient digit q t can be obtained from a six-variable string
w*ow**w*iw*iw£ 2w**, as shown in Table 9.26 for q t = 1 and Table 9.27 for
q ( = I. Using the Karnaugh map, we can derive the minimized logical expres-
sions for outputs 1 and I of the quotient digits as shown below.

for output 1: w**w*i + w**wf <2 + w^ 0 w^fvvf 2 , (9.63)

for output I: w* ()wf tf + w* 0wf^ + wf^wf^wf^, (9.64)

Table 9.26
Encodings of w it0w ittw ii2 Generating a Quotient Digit 1 [145]
'i,l W i,2 W *,0 W** W*l W*l Wf

1 0 1 0 1 0 0 0 1
1 0 0 0 1 0 0 0 0
1 0 I 0 1 0 0 1 0
! 1 1 0 1 1 0 0 1
1 T 0 0 1 1 0 0 0
0 I 1 0 0 0 1 0 1
0 1 0 0 0 0 1 0 0