Optical reversible programmable Boolean logic unit

Tanay Chattopadhyay

doi:10.1364/AO.51.005266

Applied Optics
Vol. 51,
Issue 21,
pp. 5266-5271
(2012)
•https://doi.org/10.1364/AO.51.005266

Optical reversible programmable Boolean logic unit

Tanay Chattopadhyay

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Tanay Chattopadhyay, "Optical reversible programmable Boolean logic unit," Appl. Opt. 51, 5266-5271 (2012)

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Abstract

Computing with reversibility is the only way to avoid dissipation of energy associated with bit erase. So, a reversible microprocessor is required for future computing. In this paper, a design of a simple all-optical reversible programmable processor is proposed using a polarizing beam splitter, liquid crystal-phase spatial light modulators, a half-wave plate, and plane mirrors. This circuit can perform 16 logical operations according to three programming inputs. Also, inputs can be easily recovered from the outputs. It is named the “reversible programmable Boolean logic unit (RPBLU).” The logic unit is the basic building block of many complex computational operations. Hence the design is important in sense. Two orthogonally polarized lights are defined here as two logical states, respectively.

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	Logical States of the Electrical Inputs		Optical Outputs
Inputs	$A$	$B$	$O 1$	$O 2$	$O 3$
$I 1 = s$ -polarized light	0	0	s	s	p
$I 2 = s$ -polarized light	0	1	s	p	s
$I 3 = p$ -polarized light	1	0	s	s	p
${P, Q, R = A, B, A}$	1	1	p	s	s
			$(\bar{A} + \bar{B})$	$(A + \bar{B})$	$B$

Optical Inputs			Electrical Inputs			Optical Outputs
$I 1$	$I 2$	$I 3$	$P$	$Q$	$R$	$O 1$	$O 2$	$O 3$
0	0	1	$A$	$B$	$A$	$A B$	$\bar{A} B$	$\bar{B}$
0	1	0				0	$(A + \bar{B})$	$\bar{A} B$
0	1	1				$A B$	1	$(\bar{A} + \bar{B})$
1	0	0				$(\bar{A} + \bar{B})$	0	$A B$
1	0	1				1	$\bar{A} B$	$(A + \bar{B})$
1	1	0				$(\bar{A} + \bar{B})$	$(A + \bar{B})$	$B$
0	0	1	$A$	$B$	$B$	$B$	0	$\bar{B}$
0	1	0				$A \bar{B}$	$(A ⊙ B)$	$\bar{A} B$
0	1	1				$(A + B)$	$(A ⊙ B)$	$(\bar{A} + \bar{B})$
1	0	0				$\bar{A} \bar{B}$	$(A \otimes B)$	$A B$
1	0	1				$(\bar{A} + B)$	$(A ⊙ B)$	$(A + \bar{B})$
1	1	0				$\bar{B}$	1	$B$
1	0	0	$A$	$A$	$B$	$\bar{A} \bar{B}$	$\bar{A} B$	$A$
			$A$	$A$	$A$	$\bar{A}$	0	$A$
			$B$	$B$	$B$	$\bar{B}$	0	$B$
			$B$	$A$	$B$	$(\bar{A} + \bar{B})$	0	$A B$
			$B$	$A$	$A$	$(\bar{A} + \bar{B})$	$(A ⊙ B)$	$A B$

	Logical States of the Electrical Inputs		Optical Outputs
Inputs	$A$	$B$	$O 1$	$O 2$	$O 3$
$I 1 = s$ -polarized light	0	0	s	s	p
$I 2 = s$ -polarized light	0	1	s	p	s
$I 3 = p$ -polarized light	1	0	s	s	p
${P, Q, R = A, B, A}$	1	1	p	s	s
			$(\bar{A} + \bar{B})$	$(A + \bar{B})$	$B$

Optical Inputs			Electrical Inputs			Optical Outputs
$I 1$	$I 2$	$I 3$	$P$	$Q$	$R$	$O 1$	$O 2$	$O 3$
0	0	1	$A$	$B$	$A$	$A B$	$\bar{A} B$	$\bar{B}$
0	1	0				0	$(A + \bar{B})$	$\bar{A} B$
0	1	1				$A B$	1	$(\bar{A} + \bar{B})$
1	0	0				$(\bar{A} + \bar{B})$	0	$A B$
1	0	1				1	$\bar{A} B$	$(A + \bar{B})$
1	1	0				$(\bar{A} + \bar{B})$	$(A + \bar{B})$	$B$
0	0	1	$A$	$B$	$B$	$B$	0	$\bar{B}$
0	1	0				$A \bar{B}$	$(A ⊙ B)$	$\bar{A} B$
0	1	1				$(A + B)$	$(A ⊙ B)$	$(\bar{A} + \bar{B})$
1	0	0				$\bar{A} \bar{B}$	$(A \otimes B)$	$A B$
1	0	1				$(\bar{A} + B)$	$(A ⊙ B)$	$(A + \bar{B})$
1	1	0				$\bar{B}$	1	$B$
1	0	0	$A$	$A$	$B$	$\bar{A} \bar{B}$	$\bar{A} B$	$A$
			$A$	$A$	$A$	$\bar{A}$	0	$A$
			$B$	$B$	$B$	$\bar{B}$	0	$B$
			$B$	$A$	$B$	$(\bar{A} + \bar{B})$	0	$A B$
			$B$	$A$	$A$	$(\bar{A} + \bar{B})$	$(A ⊙ B)$	$A B$

Abstract

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Applied Optics