### Integer vitae

Here is a small sequence of the integers around zero listed in the usual way--in sequence in ascending order. So the only question is: What &\$#@*&!*\$ numeration (system of representing numbers) did I use?

…, 1010, 1011, 1000, 1001, 1110, 1111, 1100, 1101, 10, 11, 0, 1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, 11110, ...

1. Around zero, as: -4,-3,-2,-1,0,1,2,3,4 are around zero?

Every eighth number seems to share a pattern, but it's not clear. I assume 0 is zero, but I'm not sure I understand the formulation of the problem.

2. Are there negative numbers in the list? Have you dropped the signs or are they encoded too? They appear to be base four couplets, but it's 1AM, I just finished a lot of work, and my brain is dead.

Substituting as follows:
A=10
B=11
C=00
D=01

which has enough in common with counting to make me think I'm close, but I'd be more convinced if D was followed by BA.

3. Good job, guys. I think it's already time for a hint, er, clarification. The twenty-one numerals represent -10 through 10 in sequence, and "0" is indeed 0. The representation shown for -10 means -10; i.e., signs are in some sense encoded.

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