1's complement and 2's complement


#1

Assuming all numbers are in 2’s complement representation,which of the following numbers is divisible by 11111011?

A)11100111
B)11100100
C)11010111
D)11011011


#2

The answer is A)11100111. Remember that 2’s complement of a 2’s complement of the number is the number itself.
Now, since all the given numbers are in 2’s complement already, first you will have to convert the number into simple binary numbers by doing 2’s complement of all the numbers (in question and options). Then, we get to know that the divisibility to be checked is of 5 (11111011’s 2’s complement is 00000101). Now, we see each option if it is divisible by 5 or not.
Option A on 2’s complementing will become 00011001 i.e. 25 which is divisible by 5.