I am trying to set up a Cisco 503 router with IOS version 12.2 stored in the TFTP server (the router already has IOS version 11.1 stored on it). I am able to copy the IOS onto a TFTP server, but when I give the command to boot the router from the TFTP, it starts booting, but after 86% completion it says "buffer overflow." Is it possible to boot a new version of IOS without deleting the older version of IOS or should I delete the older version and only then boot the new version of IOS? While booting from the TFTP server, does it store some amount of info on the router memory?
You are running low on memory. Try an IOS which has lesser requirements. You can have any number of images till memory (DRAM as well as flash) requirements are met. After that you start getting error messages like the one you describe.
TFTP will load any info on router memory, only it is the router that keeps a track of IP addresses, etc. and pointer for the image.
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