Final answer:
The question seems to refer to a binary encoding system with multiple representations for zero, which does not align with common binary systems like two's complement. Excess-3 code is one such system that has extra representations but doesn't match the description given. The provided reasoning appears to discuss a rounding system rather than a binary coding system.
Step-by-step explanation:
The integer decoding scheme in question appears to refer to a binary representation system where a single value (in this case, the number 0) can be represented in more than one way. This is indicative of a redundant representation system. However, the typical binary systems used in computers, such as the two's complement, do not have redundant zero representations. On the other hand, one known binary coding system that does allow for multiple representations of zero is the excess-3 or XS-3 code, which is a non-weighted code used primarily in digital systems.
In the excess-3 code system, the decimal number is first increased by three, and then the resulting number is represented in binary. When decoding, the binary number is converted back to decimal and then decreased by three to find the original number. Because the encoding process starts at 3 rather than 0, it means that there are binary representations for negative numbers, just not necessarily the way two's complement does it. Still, the details provided in the reasoning do not accurately describe a well-known integer decoding scheme and seem to refer to a system of rounding rather than binary encoding. Therefore, I'm unable to confirm a known system that matches the description precisely.