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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

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