A positive binary number is even precisely when its last dig

Solution

The answer is a negative 2\'s complement is even when the last digit is 0.
To prove it let us assume there is negative 2\'s compliment even number which ends with 1. Hence we can write the number as
1...1 = -(2\' complement of 1..1)
= -(0..1)
   which is not even.
And as we know that a positive binary number when ends with 1 is not even, hence by contradiction proofs that negative 2\'s complement is even when the last digit is 0