Page 511 - Introduction to Information Optics

9. Computing with Optics

Table 9.5
Truth Table for Unified Negabinary
Addition/Subtraction [55]

0 0 0 0 0 0
0 0 ] 0 0 1
1 0 0 0 0 1
i 0 I 0 1 0
0 1 0 1 0 1
0 1 1 0 0 0

For addition:

,, + (0) _ L (9.Ha)
LI f t-,
,,-(0) A /; -1).
<-i ~ U, (I — -M, 1,0,
For subtraction:

= a,,
(9.14b)
-1,0, !,...,#- 1).

After the initialization, both addition and subtraction of two numbers can be
carried out in parallel by the successive use of the same substitution rules listed
above. At each iteration, at least 1 bit of the final result for a pair of operands
can be obtained. Therefore, a unified symbolic arithmetic for addition and
subtraction has been established.
For clarity and without the loss of generality, addition of the 4-bit integral
numbers A = (3) 10 = (0111)_ 2 and B — ( — 6) 10 = (1110)_ 2, and subtraction
of the numbers A =(-3) 10 = (1101)_ 2 and B = (-9) 10 = (1011)_ 2 are illus-
trated below:

-6111 0 0000 0 1
3011 1 100 1 010 1 110 1 (=-3 10 )
000 0 011 0 0 0

0000 001 0 0 0
-3 110 1 011 0 001 0 1 101 0
) - 9 101 1 000 0 0 1 (=610)