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+18 votes

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

  1. $11100111$

  2. $11100100$

  3. $11010111$

  4. $11011011$

in Digital Logic by Veteran (52.1k points)
edited by | 2.3k views

4 Answers

+20 votes
Best answer

MSB of $2$'s compliment number has a weight of - $2^{(n-1)}$

( Trick: (from reversing sign extension) just skip all leading $1$'s from MSB expect but $1$, and then calculate the value as normal signed binary rep. )

so by calculating, we get the given number is $-5$ in decimal. and options are 

  1. $-25$
  2. $-28$
  3. $-41$
  4. $-37$

Therefore it is clear that $- 25$ is divisible by $- 5$. so we can say that (A) is correct 😄

by Active (2.7k points)
edited by
can u explain these trick by taking any example

+15 votes

Each no is in 2's complement so Lets first convert everything into decimal then it would be easy to see what is wrong  or what is right.

1 .you first check if the number is negative or positive by looking at the sign bit.

2. If it is positive, simply convert it to decimal. If it is negative, make it positive by inverting the bits and adding one.

3 . Then, convert the result to decimal. The negative of this number is the value of the original binary.

Interpret 11111011 as a two's complement binary number, and give its decimal equivalent

  1. First, note that the number is negative, since it starts with a 1.
  2. Change the sign to get the magnitude of the number.

Simply take the 2's complement of the number.(I think you guys know how to do that then its a cake walk)

2's complement of 11111011  is  00000101  and if you convert it in to Decimal it would be -5

similarly do with all options then we get

11100111 as -25

11100100 as -28

11010111 as -41 and

11011011 as -37  Now you know what should be the answer.

Note -Since the original number was negative, the final result is Negative

by Boss (45.2k points)
Why are you changing the sign bit while converting the number from 2's complemented form to sign magnitude form?

Ex: 2's complement of 11111011  is  10000101 and not this 00000101.
+4 votes

No. Is - 5 and a is -25
by Loyal (8.2k points)
–1 vote
This is a pretty confusing one here even the divisor is 2 complemented so it will be option a.
by Active (3.3k points)

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