Without an existing system it would be slow, but possible. I often teach people to memorize the order of black and red in a deck of cards forwards and backwards

Without an existing system it would be slow, but possible. I often teach people to memorize the order of black and red in a deck of cards forwards and backwards within 15-20 minutes, even if they have no previous experience or system. (The equivalent of 52 random binary digits.) Memorizing binary data is significantly easier though.