NIMCET 2009 Question Paper with solutions

Question : 101 of 120

Marks: +1, -0

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

Solution:

1's complement of 11111011 is

=00000100

Now, it's 2's complement

=00000100

\;\;\;+\;\;\;\;\;\;\;\;\;\;1

\;\;\;───────

\;\;\;\;\;\00000101

\;\;\;───────

Its Decimal equivalent

=1 × 2^{2}+0 × 2^{1}+1 × 2^{0}=4+0+1=5

From option 0 ;
1's complement of 00000110 is

=11111001

Now, it's

2^{'}

s complement

=111110011

\;\;\;\;+\;\;\;\;\;\;\;\;\;\;1

\;\;\;───────

\;\;\;\;\;\;11111010

\;\;\;───────

Its decimal equivalent

=1 × 2^{7}+1 × 2^{6}+1 × 2^{5}+1 × 2^{4}+ 1 × 2^{3} +0 × 2^{2}+.1 × 2^{1}+0 × 2^{0}

=128+64+32+16+8+2=250

which is divisible by 5 .

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