Digital optical adder based on spatial filtering

Adolf W. Lohmann; J. Weigelt

doi:10.1364/AO.25.003047

Applied Optics
Vol. 25,
Issue 18,
pp. 3047-3053
(1986)
•https://doi.org/10.1364/AO.25.003047

Digital optical adder based on spatial filtering

Adolf W. Lohmann and J. Weigelt

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Adolf W. Lohmann and J. Weigelt, "Digital optical adder based on spatial filtering," Appl. Opt. 25, 3047-3053 (1986)

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Abstract

The optical implementation of a half adder is presented, and its extension to a full adder and a ripple carry adder is described. The adder is based on a spatial filtering method using theta modulation for encoding of the binary data. Many pairs of numbers can be added in parallel. Nonreal-time laboratory experiments are described, and experimental results are shown.

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A_i	B_i	C_i	CARRY	SUM
A_i	B_i	C_i	$\begin{array}{l} C_{i + 1} = (A_{i} AND B_{i}) OR (B_{i} AND C_{i}) OR (C_{i} AND A_{i}) \\ = {\begin{array}{l} A_{i} & AND & B_{i} & for & C_{i} = 0 \\ A_{i} & OR & B_{i} & for & C_{i} = 1 \end{array} \end{array}$	$\begin{array}{l} S_{i} = A_{i} XOR B_{i} XOR C_{i} \\ = {\begin{array}{l} A_{i} XOR B_{i} & for & C_{i} = 0 \\ A_{i} EQV B_{i} & for & C_{i} = 1 \end{array} \end{array}$

0	0	0	0	0
0	1	0	0	1
1	0	0	0	1
1	1	0	1	0
0	0	1	0	1
0	1	1	1	0
1	0	1	1	0
1	1	1	1	1

A_i	B_i	C_i	CARRY	SUM
A_i	B_i	C_i	$\begin{array}{l} C_{i + 1} = (A_{i} AND B_{i}) OR (B_{i} AND C_{i}) OR (C_{i} AND A_{i}) \\ = {\begin{array}{l} A_{i} & AND & B_{i} & for & C_{i} = 0 \\ A_{i} & OR & B_{i} & for & C_{i} = 1 \end{array} \end{array}$	$\begin{array}{l} S_{i} = A_{i} XOR B_{i} XOR C_{i} \\ = {\begin{array}{l} A_{i} XOR B_{i} & for & C_{i} = 0 \\ A_{i} EQV B_{i} & for & C_{i} = 1 \end{array} \end{array}$

0	0	0	0	0
0	1	0	0	1
1	0	0	0	1
1	1	0	1	0
0	0	1	0	1
0	1	1	1	0
1	0	1	1	0
1	1	1	1	1

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Equations (5)

Applied Optics