Final answer:
When a binary odometer with all ones rolls over, it goes back to all zeros; this is known as a binary overflow. This reflects the base-2 system, where a bit can only be 0 or 1, and rollover is the result of exceeding the maximum value the binary number can hold.
Step-by-step explanation:
If you let a binary odometer go all the way to all-ones (like 111111 in binary) and then keep going, it will roll over to all-zeros (like 000000 in binary), similar to how a traditional decimal odometer rolls over after reaching its maximum count. In binary, this rollover happens because binary counting follows the base-2 numeral system, where each digit (bit) can only have two values: 0 or 1. Once all bits are at their maximum value (1), adding one more (incrementing) causes a cascade of carries that sets all bits back to zero, and often an extra bit is added at the leftmost side, just as in decimal where a 1 would be added to a new column after a 999999 odometer rolls over to 000000.
This process is a fundamental aspect of how computers work with numbers, and it's known as a binary overflow in the context of computer science and digital electronics. Specifically, in cases where a fixed-size binary number is being used (like an 8-bit byte), the overflow can mean that the system cannot represent numbers beyond a certain point and wraps around to zero. Understanding this principle is important for grasping how computers perform arithmetic operations and manage numerical data.