The reason is because hexdump by default prints out 16-bit integers, not bytes. If your system has them, hd (or hexdump -C) or xxd will provide less surprising outputs – if not, od -t x1 is a POSIX-standard way to get byte-by-byte hex output. You can use od -t x1c to show both the byte hex values and the corresponding letters.
If you have xxd (which ships with vim), you can use xxd -r to convert back from hex (from the same format xxd produces). If you just have plain hex (just the ‘4161’, which is produced by xxd -p) you can use xxd -r -p to convert back.