Implementation of trinary logic in a polarization encoded optical shadow-casting scheme

Rizwan A. Rizvi; K. Zaheer; M. Suhail Zubairy

doi:10.1364/AO.30.000936

Applied Optics
Vol. 30,
Issue 8,
pp. 936-942
(1991)
•https://doi.org/10.1364/AO.30.000936

Implementation of trinary logic in a polarization encoded optical shadow-casting scheme

Rizwan A. Rizvi, K. Zaheer, and M. Suhail Zubairy

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Rizwan A. Rizvi, K. Zaheer, and M. Suhail Zubairy, "Implementation of trinary logic in a polarization encoded optical shadow-casting scheme," Appl. Opt. 30, 936-942 (1991)

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Abstract

The design of various multioutput trinary combinational logic units by a polarization encoded optical shadow-casting (POSC) technique is presented. The POSC modified algorithm is employed to design and implement these logic elements in a trinary number system with separate and simultaneous generation of outputs. A detailed solution of the POSC logic equations for a fixed source plane and a fixed decoding mask is given to obtain input pixel coding for a trinary half-adder, full adder, and subtractor.

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Equations (50)

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Condition number	A	B	C	S	C′
1	0	0	0	0	0
2	0	0	1	1	0
3	0	1	0	1	0
4	1	0	0	1	0
5	1	1	0	2	0
6	1	0	1	2	0
7	0	1	1	2	0
8	0	2	0	2	0
9	2	0	0	2	0
10	1	2	0	0	1
11	2	1	0	0	1
12	0	2	1	0	1
13	2	0	1	0	1
14	1	1	1	0	1
15	2	1	1	1	1
16	1	2	1	1	1
17	2	2	0	1	1
18	2	2	1	2	1

Condition number	A	B	C	D	B′
1	0	0	0	0	0
2	1	1	0	0	0
3	1	0	1	0	0
4	2	1	1	0	0
5	2	2	0	0	0
6	0	0	1	2	1
7	0	1	0	2	1
8	1	2	0	2	1
9	1	1	1	2	1
10	2	2	1	2	1
11	0	1	1	1	1
12	0	2	0	1	1
13	1	2	1	1	1
14	1	0	0	1	0
15	2	1	0	1	0
16	2	0	1	1	0
17	0	2	1	0	1
18	2	0	0	2	0

Condition number	A	B	C	S	C′
1	0	0	0	0	0
2	0	0	1	1	0
3	0	1	0	1	0
4	1	0	0	1	0
5	1	1	0	2	0
6	1	0	1	2	0
7	0	1	1	2	0
8	0	2	0	2	0
9	2	0	0	2	0
10	1	2	0	0	1
11	2	1	0	0	1
12	0	2	1	0	1
13	2	0	1	0	1
14	1	1	1	0	1
15	2	1	1	1	1
16	1	2	1	1	1
17	2	2	0	1	1
18	2	2	1	2	1

Condition number	A	B	C	D	B′
1	0	0	0	0	0
2	1	1	0	0	0
3	1	0	1	0	0
4	2	1	1	0	0
5	2	2	0	0	0
6	0	0	1	2	1
7	0	1	0	2	1
8	1	2	0	2	1
9	1	1	1	2	1
10	2	2	1	2	1
11	0	1	1	1	1
12	0	2	0	1	1
13	1	2	1	1	1
14	1	0	0	1	0
15	2	1	0	1	0
16	2	0	1	1	0
17	0	2	1	0	1
18	2	0	0	2	0

Condition number	A	B	C	S	C′
1	0	0	0	0	0
2	0	0	1	1	0
3	0	1	0	1	0
4	1	0	0	1	0
5	1	1	0	2	0
6	1	0	1	2	0
7	0	1	1	2	0
8	0	2	0	2	0
9	2	0	0	2	0
10	1	2	0	0	1
11	2	1	0	0	1
12	0	2	1	0	1
13	2	0	1	0	1
14	1	1	1	0	1
15	2	1	1	1	1
16	1	2	1	1	1
17	2	2	0	1	1
18	2	2	1	2	1

Condition number	A	B	C	D	B′
1	0	0	0	0	0
2	1	1	0	0	0
3	1	0	1	0	0
4	2	1	1	0	0
5	2	2	0	0	0
6	0	0	1	2	1
7	0	1	0	2	1
8	1	2	0	2	1
9	1	1	1	2	1
10	2	2	1	2	1
11	0	1	1	1	1
12	0	2	0	1	1
13	1	2	1	1	1
14	1	0	0	1	0
15	2	1	0	1	0
16	2	0	1	1	0
17	0	2	1	0	1
18	2	0	0	2	0

Condition number	A	B	C	S	C′
1	0	0	0	0	0
2	0	0	1	1	0
3	0	1	0	1	0
4	1	0	0	1	0
5	1	1	0	2	0
6	1	0	1	2	0
7	0	1	1	2	0
8	0	2	0	2	0
9	2	0	0	2	0
10	1	2	0	0	1
11	2	1	0	0	1
12	0	2	1	0	1
13	2	0	1	0	1
14	1	1	1	0	1
15	2	1	1	1	1
16	1	2	1	1	1
17	2	2	0	1	1
18	2	2	1	2	1

Condition number	A	B	C	D	B′
1	0	0	0	0	0
2	1	1	0	0	0
3	1	0	1	0	0
4	2	1	1	0	0
5	2	2	0	0	0
6	0	0	1	2	1
7	0	1	0	2	1
8	1	2	0	2	1
9	1	1	1	2	1
10	2	2	1	2	1
11	0	1	1	1	1
12	0	2	0	1	1
13	1	2	1	1	1
14	1	0	0	1	0
15	2	1	0	1	0
16	2	0	1	1	0
17	0	2	1	0	1
18	2	0	0	2	0

Condition number	A	B	C	S	C′
1	0	0	0	0	0
2	0	0	1	1	0
3	0	1	0	1	0
4	1	0	0	1	0
5	1	1	0	2	0
6	1	0	1	2	0
7	0	1	1	2	0
8	0	2	0	2	0
9	2	0	0	2	0
10	1	2	0	0	1
11	2	1	0	0	1
12	0	2	1	0	1
13	2	0	1	0	1
14	1	1	1	0	1
15	2	1	1	1	1
16	1	2	1	1	1
17	2	2	0	1	1
18	2	2	1	2	1

Condition number	A	B	C	D	B′
1	0	0	0	0	0
2	1	1	0	0	0
3	1	0	1	0	0
4	2	1	1	0	0
5	2	2	0	0	0
6	0	0	1	2	1
7	0	1	0	2	1
8	1	2	0	2	1
9	1	1	1	2	1
10	2	2	1	2	1
11	0	1	1	1	1
12	0	2	0	1	1
13	1	2	1	1	1
14	1	0	0	1	0
15	2	1	0	1	0
16	2	0	1	1	0
17	0	2	1	0	1
18	2	0	0	2	0

Condition number	A	B	C	S	C′
1	0	0	0	0	0
2	0	0	1	1	0
3	0	1	0	1	0
4	1	0	0	1	0
5	1	1	0	2	0
6	1	0	1	2	0
7	0	1	1	2	0
8	0	2	0	2	0
9	2	0	0	2	0
10	1	2	0	0	1
11	2	1	0	0	1
12	0	2	1	0	1
13	2	0	1	0	1
14	1	1	1	0	1
15	2	1	1	1	1
16	1	2	1	1	1
17	2	2	0	1	1
18	2	2	1	2	1

Condition number	A	B	C	D	B′
1	0	0	0	0	0
2	1	1	0	0	0
3	1	0	1	0	0
4	2	1	1	0	0
5	2	2	0	0	0
6	0	0	1	2	1
7	0	1	0	2	1
8	1	2	0	2	1
9	1	1	1	2	1
10	2	2	1	2	1
11	0	1	1	1	1
12	0	2	0	1	1
13	1	2	1	1	1
14	1	0	0	1	0
15	2	1	0	1	0
16	2	0	1	1	0
17	0	2	1	0	1
18	2	0	0	2	0

Abstract

Cited By

Figures (5)

Tables (4)

Equations (50)

Applied Optics

Condition number	A	B	C	S	C′
1	0	0	0	0	0
2	0	0	1	1	0
3	0	1	0	1	0
4	1	0	0	1	0
5	1	1	0	2	0
6	1	0	1	2	0
7	0	1	1	2	0
8	0	2	0	2	0
9	2	0	0	2	0
10	1	2	0	0	1
11	2	1	0	0	1
12	0	2	1	0	1
13	2	0	1	0	1
14	1	1	1	0	1
15	2	1	1	1	1
16	1	2	1	1	1
17	2	2	0	1	1
18	2	2	1	2	1

Condition number	A	B	C	D	B′
1	0	0	0	0	0
2	1	1	0	0	0
3	1	0	1	0	0
4	2	1	1	0	0
5	2	2	0	0	0
6	0	0	1	2	1
7	0	1	0	2	1
8	1	2	0	2	1
9	1	1	1	2	1
10	2	2	1	2	1
11	0	1	1	1	1
12	0	2	0	1	1
13	1	2	1	1	1
14	1	0	0	1	0
15	2	1	0	1	0
16	2	0	1	1	0
17	0	2	1	0	1
18	2	0	0	2	0

Condition number	A	B	C	S	C′
1	0	0	0	0	0
2	0	0	1	1	0
3	0	1	0	1	0
4	1	0	0	1	0
5	1	1	0	2	0
6	1	0	1	2	0
7	0	1	1	2	0
8	0	2	0	2	0
9	2	0	0	2	0
10	1	2	0	0	1
11	2	1	0	0	1
12	0	2	1	0	1
13	2	0	1	0	1
14	1	1	1	0	1
15	2	1	1	1	1
16	1	2	1	1	1
17	2	2	0	1	1
18	2	2	1	2	1

Condition number	A	B	C	D	B′
1	0	0	0	0	0
2	1	1	0	0	0
3	1	0	1	0	0
4	2	1	1	0	0
5	2	2	0	0	0
6	0	0	1	2	1
7	0	1	0	2	1
8	1	2	0	2	1
9	1	1	1	2	1
10	2	2	1	2	1
11	0	1	1	1	1
12	0	2	0	1	1
13	1	2	1	1	1
14	1	0	0	1	0
15	2	1	0	1	0
16	2	0	1	1	0
17	0	2	1	0	1
18	2	0	0	2	0