The base 12 computer was invented long ago. You have one on the end of your arm.
"base 12 originates from an ancient method of finger counting, first documented in Babylon, but probably much older. No, they didn't have more fingers back then. If you examine your fingers, you will see that each finger is divided into three joints. Using your thumb as a pointer, and each joint of each finger as a counter, you can count to 12 on one hand. Using the other hand to accumulate, and you easily see why numbers like 60, 360, and 144 come up so often in measurement systems."