Truth-table look-up optical processing utilizing binary and residue arithmetic

C. C. Guest; T. K. Gaylord

doi:10.1364/AO.19.001201

Applied Optics
Vol. 19,
Issue 7,
pp. 1201-1207
(1980)
•https://doi.org/10.1364/AO.19.001201

Truth-table look-up optical processing utilizing binary and residue arithmetic

C. C. Guest and T. K. Gaylord

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
C. C. Guest and T. K. Gaylord, "Truth-table look-up optical processing utilizing binary and residue arithmetic," Appl. Opt. 19, 1201-1207 (1980)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

Two possible forms of numerical truth-table look-up processors using content-addressable optical holographic memories are presented. Application of these processors to performing numerical calculations in direct binary and in binary-coded residue number systems is discussed. Specific examples of the number of input and output bits required and the number of truth-table combinations holographically recorded for computation in both numerical systems are given. Truth-table look-up processing using binary-coded residue is shown to require the recording of dramatically fewer reference patterns than direct binary.

Full Article | PDF Article

More Like This

Residue number system holographic truth-table look-up processing: detector threshold setting and probability of error due to amplitude and phase variations

M. M. Mirsalehi, C. C. Guest, and T. K. Gaylord
Appl. Opt. 22(22) 3583-3592 (1983)

Truth-table look-up parallel data processing using an optical content-addressable memory

M. M. Mirsalehi and Thomas K. Gaylord
Appl. Opt. 25(14) 2277-2283 (1986)

Number representation effects in truth-table look-up processing: 8-bit addition example

Mir M. Mirsalehi, Thomas K. Gaylord, Daniel C. Fielder, and Clark C. Guest
Appl. Opt. 28(10) 1931-1939 (1989)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (6)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (10)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

	Addition				Multiplication

	exclusive or	nand			exclusive or	nand

	One Pair of Words		m Pairs of Words		One Pair of Words		m Pairs of Words

			VERSION 1	VERSION 2			VERSION 1	VERSION 2

Number of Input Bits Per Pair of Words	2n + 1	2n + 1	2n + 1	2n + 1	2n	2n	2n	2n
Input Line/Page Composer Length During Recording	(2n + 1) (n + 1)	2n + 2	m × (2n + 2)	2n + 2	(2n)²	2n + 1	m × (2n + 1)	2n + 1
Input Line/Page Composer Length During Processing	(2n + 1) (n + 1)	2n + 2	m × (2n + 2)	(2n + 2) × m	(2n)²	2n + 1	m × (2n + 1)	(2n + 1) × m
Size of Each Stored Page	(2n + 1) (n + 1) × 2²ⁿ	(2n + 2) × 1	(2n + 2) × 1	(2n + 2) × 1	$2 n ∑_{1}^{2 n} A_{k}$	(2n + 1) × 1	(2n + 1) × 1	(2n + 1) × 1
Number of Recordings Required (Reference Beam Positions)	1	2²ⁿ × (n + 1)	2²ⁿ (n + 1) × m	2²ⁿ (n + 1)	1	$∑_{1}^{2 n} A_{k}$	$∑_{1}^{2 n} A_{k} \times m$	$∑_{1}^{2 n} A_{k}$
Size of Output Detector Array	(2n + 1) (n + 1) × 2²ⁿ	2²ⁿ × (n + 1)	2²ⁿ(n + 1) × m	2²ⁿ(n + 1) × m	$2 n ∑_{1}^{2 n} A_{k}$	$∑_{1}^{2 n} A_{k}$	$∑_{1}^{2 n} A_{k} \times m$	$∑_{1}^{2 n} A_{k} \times m$
Number of Output Bits Per Pair of Words	n + 1	n + 1	n + 1	n + 1	2n	2n	2n	2n

n	$∑_{1}^{2 n} A_{k}$
1	1
2	14
3	111
4	678
5	3,733
6	18,953
7	92,334
8	434,600

		Binary Coded Residue System with Moduli 4, 5, 7, 9	Direct Binary nearest equivalent	Binary Coded Residue System with Moduli 4, 5, 7, 9, 11, 13	Direct Binary nearest equivalent

	Range of Each Word	0–1,259	0–1,023	0–180,179	0–131,071
	Number of Bits to Represent Word	12	10	20	17

Addition	Number of Input Bits for Addition	24	21	40	35
	Number of Combinations Recorded for Addition	221	1.2 × 10⁷	694	3.1 × 10¹¹
	Number of Output Bits for Addition	12	11	20	18

Multiplication	Number of Input Bits for Multiplication	24	20	40	34
	Number of Combinations Recorded for Multiplication	186	9.1 × 10⁶	620	2.7 × 10¹¹
	Number of Output Bits for Multiplication	12	20	20	34

	Addition				Multiplication

	exclusive or	nand			exclusive or	nand

	One Pair of Words		m Pairs of Words		One Pair of Words		m Pairs of Words

			VERSION 1	VERSION 2			VERSION 1	VERSION 2

Number of Input Bits Per Pair of Words	2n + 1	2n + 1	2n + 1	2n + 1	2n	2n	2n	2n
Input Line/Page Composer Length During Recording	(2n + 1) (n + 1)	2n + 2	m × (2n + 2)	2n + 2	(2n)²	2n + 1	m × (2n + 1)	2n + 1
Input Line/Page Composer Length During Processing	(2n + 1) (n + 1)	2n + 2	m × (2n + 2)	(2n + 2) × m	(2n)²	2n + 1	m × (2n + 1)	(2n + 1) × m
Size of Each Stored Page	(2n + 1) (n + 1) × 2²ⁿ	(2n + 2) × 1	(2n + 2) × 1	(2n + 2) × 1	$2 n ∑_{1}^{2 n} A_{k}$	(2n + 1) × 1	(2n + 1) × 1	(2n + 1) × 1
Number of Recordings Required (Reference Beam Positions)	1	2²ⁿ × (n + 1)	2²ⁿ (n + 1) × m	2²ⁿ (n + 1)	1	$∑_{1}^{2 n} A_{k}$	$∑_{1}^{2 n} A_{k} \times m$	$∑_{1}^{2 n} A_{k}$
Size of Output Detector Array	(2n + 1) (n + 1) × 2²ⁿ	2²ⁿ × (n + 1)	2²ⁿ(n + 1) × m	2²ⁿ(n + 1) × m	$2 n ∑_{1}^{2 n} A_{k}$	$∑_{1}^{2 n} A_{k}$	$∑_{1}^{2 n} A_{k} \times m$	$∑_{1}^{2 n} A_{k} \times m$
Number of Output Bits Per Pair of Words	n + 1	n + 1	n + 1	n + 1	2n	2n	2n	2n

n	$∑_{1}^{2 n} A_{k}$
1	1
2	14
3	111
4	678
5	3,733
6	18,953
7	92,334
8	434,600

Abstract

Cited By

Figures (6)

Tables (3)

Equations (10)

Applied Optics