The heartbreaking reality is that the old FD and FL series lenses CAN be used with newer DSLRs, but an adapter is needed to convert it to the EF mount used by DSLRs. That will get them properly mounted to the new camera. Some adapters have an internal lens or two to correct for the distance change to the sensor. Some are nothing more than extension tubes with different mounts on each end. Each has it's benefits and drawbacks. Alternatively, there are one or more small businesses that will physically put an EF mount on an FD mount lens for a fee.
The issue, however, is the auto-focusing system within the DSLRs. Without the internal mechanisms of newer AF lenses, you will have to manually focus each of your pictures. The difficulty with manual focusing is there is not a split-ring focusing screen (or any other kind) that comes standard in a DSLR. Several types can be purchased and installed (either by yourself or trained technician) that will solve that problem. Alternatively, using Live View mode, especially with zooming in capability, you can focus quite well...on more-or-less stationary subects. But Live View can't use the split ring focusing screen, as it uses the sensor itself for the image.
Some photographers are more than willing to use an FD-to-EF adapter and manually focus, especially when using long to super telephoto focal lengths. The cost of a 400mm EF lens is higher than most want to pay, so adapting an FD lens of that focal length is a good solution. The same may apply to wide angle or macro lenses. Some photographers have purchased formerly very expensive super telephoto FD or FL lenses and used them with an adapter since the price of those lenses is typically less than 10 cents on a dollar
While it has been bantered around on various forums, a digital camera back for existing film cameras would be a fantastic solution. To my knowledge, no manufacturers have produced any, probably due to a very small 'market' for such a product.
Canon made EOS "film" bodies as well as EOS "digital bodies but the same EOS lenses work for both.
But your Canon A1 isn't an EOS... it uses FD lenses. The FD lenses have no electronic linkage to the camera -- they are mechanical. EOS cameras have no mechanical linkage to the camera -- they are fully electronic.
There are companies that make adapters, but you lose a lot of functionality... the camera cannot electronically control the f-stop nor does it get auto-focus. Instead you have to manually focus the lens ... except you lose the benefit of split-prism focusing systems because the DSLR is designed for electronic automatic focus so it doesn't need the split prism. That means that while it's "manual focus" only... it 's not as easy to manually focus the DSLR because it doesn't have the split prism focusing aid that your A1 has.
The the DSLR isn't a full-frame camera, then the viewfinder will be smaller and not as bright as your A1 (but it would be if your DSLR was a full-frame model.)
Take this from a guy that learned it the hard and expensive way. It is not a good idea. That said if you have some long focal length FD lenses, you may have some success. I have old 500mm and 600mm FD lenses and have adapted them to EOS.
The only adapter that is worth the trouble is http://www.edmika.com/. It is not a simple bolt on, in most cases.
None of the rest, and I have tried several are worth wasting your money or even time with. It is also not worth the trouble unless you have expensive FD glass with that red ring.
Mr. Mika's adapters are lens specific so you must get the right one for your lens. He may not have one for every lens you have.
Plus like I said, if all you have is the shorter focal length FD lenses, forget and move on. Just the way it is!