Using the signed modulo operation:
$(x\ \mathrm{mod}\ 2) = \begin{cases} 0\ \mathrm{if}\ x\ \mathrm{is\ even} \\ 1\ \mathrm{if}\ x > 0\ \mathrm{and}\ x\ \mathrm{is\ odd} \\ -1\ \mathrm{if}\ x < 0\ \mathrm{and}\ x\ \mathrm{is\ odd} \\ \end{cases}$
Using the signed modulo operation:
$(x\ \mathrm{mod}\ 2) = \begin{cases} 0\ \mathrm{if}\ x\ \mathrm{is\ even} \\ 1\ \mathrm{if}\ x > 0\ \mathrm{and}\ x\ \mathrm{is\ odd} \\ -1\ \mathrm{if}\ x < 0\ \mathrm{and}\ x\ \mathrm{is\ odd} \\ \end{cases}$