Share-Based Compensation (Schedule of Share-Based Compensation Expense) (Details) - USD ($) $ in Thousands	12 Months Ended
Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	$ 5,681	$ 6,528	$ 5,847
Tax benefit	(1,335)	(1,534)	(1,374)
Share-based compensation expense, net of tax	4,346	4,994	4,473
Cost Of Operating Revenues [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	257	258	142
Engineering and Research [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	210	202	207
Selling [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	577	544	419
General and Administrative [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	4,637	5,524	5,079
Operating Expenses [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	$ 5,424	$ 6,270	$ 5,705

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (h)(1)(i)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

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