Answer:
A negative 2’s complement number is even precisely when its last digit is 0 as well.
Step-by-step explanation:
Proof part 1: Assume there exists a 2’s complement negative even number which ends with 1. We can, therefore, express this number as
1 ..... 1 = - (2’s complement of 1 ....1)
= - (0 ... 1 )
≠ even
Since we know precisely that a positive binary number is not even when it ends with a 1. This is a conflict with our assumption. Our assumption is, therefore, wrong.
Proof part 2: Assume there exists a 2’s complement negative odd number which ends with 0. We can, therefore, express this number as
1 ..... 0 = - (2’s complement of 1 ....0)
= - (0 ... 0 )
= even
Since we know precisely that a positive binary number is even when it ends with a 0. This is a conflict with our assumption. Our assumption is, therefore, wrong.
