Not quite digital yet, but getting there. Books can now be ordered on line and the library will deliver them by mail. Actually, it’s a great idea for any library, although it seems to me that the logistics must be a bit complicated. You can find more at Resource Shelf.
The National Library of India will be offering an ebtire catalog of 24 lakh books on line in digital format. These books go back to the 17th and 18th centuries. As part of the library’s modernisation, the library has digitised 3,200,00 pages from 9,141 books published before 1900 in English and Indian languages. More info at Resource Shelf.