Page 584 - Introduction to Information Optics

Exercises Mi 9
EXERCISES

9.1 Design a free-space optical programmable logic array using a crossbar
switch to implement the function F(A, B, C, D) = AB + CD + DA.
9.2 Design 16 logic gates of two variables using a liquid crystal electro-optic
switch.
9.3 With reference to Fig. 9.4, design the light source patterns for all 16 logic
operations.
9.4 Perform (151) 10 — (101) 10 using residue arithmetic with the bases 5, 7,
and 11.
9.5 (a) Show how 10010011 may be added to 01100101 by means of symbolic
substitution.
(b) Derive higher-order symbolic substitution rules for 2-bit addition,
and then perform the addition in part_(a) again.
9.6 Perform MSD addition 1 lIlOlOl + IIUlll^by binary logic operations.
9.7 Perform MSD addition TTlTOlOl + 1 Till ill using the symmetrically
receded MSD algorithm.
9.8 Using the convergence MSD division algorithm, calculate the division of
X = (O.IO) MSD = (-0.5) 10 by Y = (0.11) MSD - (0.75) 10 with 16-digit pre-
cision.
9.9 Using the quotient-selected MSD divisioji jalgorithm, calculate the divi-
sion of X = (0.10lII01) MSD by y = (0.1lIoTTl) MSD.
9.10 Perform (1401) 10 — (1001 ) 10 using two-step trinary signed-digit arithmetic.
9.11 Suppose the incoherent correlator-based content-addressable memory
processor is used to implement two-step trinary signed-digit addition
(Table 9.29). Design the spatial-encoding patterns for the trinary digits
and the content-addressable memory patterns for recognition.
9.12 (a) Using the two-step quaternary signed-digit algorithm, calculate the
sum 3223 + 1212.
(b) Calculate the product 3223 x 1212.
9.13 Derive an algorithm for number conversion from the trinary signed-digit
system to the 3's complement system.
9.14 Derive an algorithm for number conversion from the quaternary signed-
digit system to the 4's complement system.
9.15 Perform negabinary signed-digit addition TllOllIl + TOOTlllI.
9.16 Convert the MSD number lOOTOOlToTTl to 2's_complement.
9.17 Convert the negabinary signed-digit number IlToTlllO to negabinary.
9.18 Design an optical system to perform matrix-vector operation for sym-
bolic substitution.
9.19 Explain how optical shifting can be accomplished with a hologram, a
polarizing beamsplitter, or a birefrigent crystal.
9.20 Design a 512x512 optical crossbar interconnection network.