The original IBM PC and XT had 16-bit CPUs (Intel 8088), as did the original IBM AT (80286). Most versions of Linux are compiled to run on at least some form of 32-bit processor, so you would need at least an Intel 80386-based computer, and even this will require an older form of Linux, or one specially-compiled for the 80386 CPU. There is at least one version of linux for 80268 computers (uclinux?), but I think that it is very limited. I think bmarkus is right in that you will need a computer with a 80486 CPU or better to run TC or almost any other modern Linux.
I think there were some Unix-like OSes or shells for the 16-bit class of computer. Early Minix I think might work. There was a commercial Unix-like OS for PCs called MKS Coherent, if you can find a copy.
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Mike L.