You've narrowed down the year to three possibilities using the AoS code. I'll help you eliminate two of those three using another important piece of information - the seal on the box.
Seals on USPC standard-issue decks come in three varieties, used at different times in history. From the early 20th-Century until 1965, the seal would have been a tax stamp, in most cases one that was printed by the Internal Revenue Service. The stamp itself would have a mark from an inked rubber stamp or (for early decks) markings in pen indicating that the stamp was canceled and can't be reused. Of course, that assumes the deck was sold in the US - as I understand it, the Aladdin brand was made especially for the Singaporean market, using a card stock designed to better withstand the extreme humidity found there.
The change from using tax stamps occurred when the Federal tax on playing cards was repealed. From 1965 until some time in the 1980s, company stamp seals were used - they looked vaguely like the tax stamps but had company logos on them instead. Two opposing sides of the four sides (I think the top and bottom) were perforated and the backs used a moisture-activated adhesive, just like old postage stamps.
Then from the 1980s to today, the stamps were replaced with stickers that were self-adhesive - they usually stuck on better, required a simpler automated process for application and they had no perforated edges on them.
For any deck with an AoS letter code of "B":
A 1921 deck would have a US tax stamp if it was sold in the US.
A 1976 deck would have a USPC stamp.
A 1996 deck would have a USPC sticker.
Your deck has a USPC sticker, ergo, it's from 1996. The bar code is an additional giveaway as to the precise year - bar-coded decks started to appear not longer after sticker seals were implemented.
It's a nice find, actually - the newer decks no longer show the "National Playing Card Company" name anywhere on the box or the Ace of Spades, only USPC. As I understand it, they 1002s were discontinued because of the cost of the gilding and the amount of labor used to apply it (it's all done manually, using small paint brushes), though overseas they can still be found if you look around. 1001s have boxes in either red or blue and they're still in production - I have some that were printed in Erlanger, KY perhaps two or three years ago. In Singapore, I'm told they're far more commonly found than Bicycle decks - they practically are the "Bicycle Rider Backs" of Singapore, while Bicycles are exotic, expensive in comparison and don't hold up well in that climate. Neither the 1002s nor the 1001s are commonly found in the US - usually they're only sold by magic shops or secondary-market playing card retailers.
Assuming the "B" code is kept as part of the regular rotation, it will appear again probably in 2016 - they cycle about every twenty years, normally, unless they're taken out of the rotation for some reason only USPC knows. That deck will be distinctive from the others because:
- it will be marked as made in Erlanger, KY
- it will have more extensive copyright information printed on the bottom of the box
- the modern AoS code has a four-digit prefix that indicates the week and year of manufacture in addition to the letter code.