Share-Based Compensation (Schedule of Share-Based Compensation Expense) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	$ 6,698	$ 5,681	$ 6,528
Tax benefit	(1,574)	(1,335)	(1,534)
Share-based compensation expense, net of tax	5,124	4,346	4,994
Cost Of Operating Revenues [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	183	257	258
Engineering and Research [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	232	210	202
Selling [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	632	577	544
General and Administrative [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	5,651	4,637	5,524
Operating Expenses [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	$ 6,515	$ 5,424	$ 6,270