Polarization-encoded optical shadow-casting arithmetic-logic-unit design: separate and simultaneous output generation

Jamal U. Ahmed; Abdul Ahad S. Awwal

doi:10.1364/AO.31.005622

Applied Optics
Vol. 31,
Issue 26,
pp. 5622-5631
(1992)
•https://doi.org/10.1364/AO.31.005622

Polarization-encoded optical shadow-casting arithmetic-logic-unit design: separate and simultaneous output generation

Jamal U. Ahmed and Abdul Ahad S. Awwal

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Jamal U. Ahmed and Abdul Ahad S. Awwal, "Polarization-encoded optical shadow-casting arithmetic-logic-unit design: separate and simultaneous output generation," Appl. Opt. 31, 5622-5631 (1992)

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Abstract

A memory-efficient dual cell and a multioutput parallel arithmetic logic unit are designed by using a polarization-encoded optical shadow-casting scheme. The design algorithms for identifying the source patterns, input encoding, and output mask are also presented.

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Control Input	Logical Operations
C	or	and	A + $\bar{B}$	A $\bar{B}$	$\bar{XOR}$	A	B	false
$\bar{C}$	nor	nand	ĀB	Ā + B	xor	Ā	$\bar{B}$	true

Output	Sharing	Nonsharing
S or D	(2, 3)	(5, 8)
C′	(4, 8)	(6, 7)
B	(2, 3), (4, 8)

Input Pixels	OR Output Pixel	Output
(1, 1), (1, 2);	(1, 2)	S or D
(1, 1), (2, 1);	(2, 1)	B
(2, 1), (2, 2);	(3, 2)	C′

Control Input	Logical Operations
C	or	and	A + $\bar{B}$	A $\bar{B}$	$\bar{XOR}$	A	B	false
C	nor	nand	ĀB	Ā + B	xor	Ā	$\bar{B}$	true

Logical Operation	Input Conditions	Logical Operation	Input Conditions
and	(8)	nand	(1, 3, 5)
or	(4, 6, 8)	nor	(1)
$\bar{XOR}$	(2, 8)	xor	(3, 5)
A	(6, 8)	Ā	(1, 3)
B	(4, 8)	$\bar{B}$	(1, 5)
A $\bar{B}$	(6)	Ā + B	(1, 3, 7)
A + $\bar{B}$	(2, 6, 8)	ĀB	(3)
false	(none of the even minterms)	true	(1, 3, 5, 7)

Input Pixel	Output Pixel	Output
(1, 1)	(1, 1)	ĀB
(1, 1), (1, 2)	(1, 2)	Sum, xor, $\bar{XOR}$
(1,2), (1,3)	(1,3)	and, $\bar{B}$
(1, 3)	(1, 4)	nor
(1, 1), (1, 2), (2, 1), (2, 2)	(2, 2)	A + $\bar{B}$
(1, 2), (1, 3), (2, 2), (2, 3)	(2, 3)	true, A
(1, 3), (2, 3)	(2, 4)	nand, false
(2, 1)	(3, 1)	B
(2, 1), (2, 2)	(3, 2)	or
(2, 2), (2, 3)	(3, 3)	Ā + B, A $\bar{B}$
(2, 3)	(3, 4)	Ā

Output Operations	Input Conditions	Primry Input		Primay Code	Secondary Input C	Output

		A	B
Sum (S)	1	0	0	V	1	1
Difference (D)	2	1	1	H	1	1
	3	0	1	V	0	1
	4	1	0	H	0	1
Carry-out (C′)	1	0	0	V	X	0
	2	1	1	H	X	1
	3	0	1	V	1	1
	4	1	0	H	1	1
Borrow-out (B)	1	0	0	V	1	1
	2	1	1	H	1	1
	3	0	1	V	X	1
	4	1	0	H	X	0

		Code

Logical Operations		C	$\bar{C}$
or	nor	$(\begin{matrix} H \\ T \end{matrix})$	$(\begin{matrix} V \\ F \end{matrix})$
and	nand	$(\begin{matrix} H \\ F \end{matrix})$	$(\begin{matrix} V \\ T \end{matrix})$
$\bar{XOR}$	xor	$(\begin{matrix} T \\ F \end{matrix})$	$(\begin{matrix} F \\ T \end{matrix})$
A	Ā	$(\begin{matrix} H \\ H \end{matrix})$	$(\begin{matrix} V \\ V \end{matrix})$
B	$\bar{B}$	$(\begin{matrix} H \\ V \end{matrix})$	$(\begin{matrix} V \\ H \end{matrix})$
A + $\bar{B}$	ĀB	$(\begin{matrix} T \\ H \end{matrix})$	$(\begin{matrix} F \\ V \end{matrix})$
A $\bar{B}$	Ā + B	$(\begin{matrix} F \\ H \end{matrix})$	$(\begin{matrix} T \\ V \end{matrix})$
false	true	$(\begin{matrix} F \\ F \end{matrix})$	$(\begin{matrix} T \\ T \end{matrix})$

	Pixel Code

Input	1	0
A	$(\begin{matrix} F & T & V \\ H & T & F \end{matrix})$	$(\begin{matrix} T & F & H \\ V & F & T \end{matrix})$
B	$(\begin{matrix} V & H & F \\ T & V & V \end{matrix})$	$(\begin{matrix} H & V & T \\ F & H & H \end{matrix})$
C	$(\begin{matrix} H & H & F \\ T & H & F \end{matrix})$	$(\begin{matrix} V & V & T \\ F & V & T \end{matrix})$

Abstract

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Equations (31)

Applied Optics