Write the conjunctive or disjunctive normal form of an expression $f$ [closed]

Write the conjunctive or disjunctive normal form of an expression $f$ that is true if the number $t=(xyz)_2$ is a zero of the following polynomial:

$$p(t)=(t-6)(t-5)(t-4)(t-2)t(t+1)(t+3)(t+7)$$

The zeros of this polynomial are $-7,-3,-1,0,2,4,5,6$. So $t$ has to be $(000)_2$ or $(010)_2$ or $(100)_2$ or $(101)_2$ or $(110)_2$ or... But now I don't know how to represent these negative numbers in binary? In other words how do I write $-7,-3,-1$ in the form $(xyz)_2$?

• I don't think we can help you -- this is something you need to be asking whoever set you the question. In particular, no natural three-bit datatype can represent that set of numbers. Commented Nov 29, 2016 at 16:54

As @DavidRicherby said, it's best if you ask who-gave-you-the-question what he meant by $(xyz)_2$. But if you absolutely can not do that, then you look at the situation mathematically as...
$(xyz)_2$ here is a set $\{000,001,010,011,...,111\}$ of $8$ elements which forms a ring. In particular, it supports two binary operation $+$ and $\times$ where both operation has identity element, the addition has inverses...