edited by
12,114 views
34 votes
34 votes
The $16\text{-bit}\;2's$ complement representation of an integer is $1111 \quad 1111 \quad 1111 \quad 0101;$ its decimal representation is ____________
edited by

9 Answers

Best answer
45 votes
45 votes
$1111 \; 1111\; 1111\; 0101$

$2's$ complement of $1111 \; 1111\; 1111\; 0101 = 0000 \; 0000\; 0000\; 1011 =+11$

$2's$ complement of $-11 = +11,$ in $2's$ complement representation

$2's$ complement of $+11 = -11,$ in $2's$ complement representation

So $-11$ it should be.
edited by
37 votes
37 votes

Answer $= -11$.

for $2's$ complement  1 111 1111 1111 0101  $→$$2′s$ complement$→$$2′s$ complement  $1$ $000$  $0000$  $0000$  $1011$

1bit$^{st}$ is same not involved in $2's$ complement same with $1's$ complement. since msb bit for sign.

Take one's complement and add $1$ we get $11$, and as it is negative number we get answer as $-11$.

Reference: http://www.electronics-tutorials.ws/binary/signed-binary-numbers.html.

edited by
14 votes
14 votes

   1111111111110101  -> ignore all 1's, except one 1 from left side(because they have no effect on final decimal value)

=  10101

=  (-24)*1 + (23)*0 + (22)*1 + (21)*0 + (20)*1  

= -16 + 4 + 1

= -11

2 votes
2 votes
Procedure:

Consider the power place values ofthe number from right to left is 0,1,2,3,4,5........ so on

Calculate the place value of first 1 of the number from left where contineous 1s are there to the left of it till end(Let called the place i).

Then do this formula: -(2^i)+(sum of all 2^j)   Here j is from i-1  to 0

Here Number is:1111111111110101

  -(2^4) +2^2+2^0=-16+4+1=-11
Answer:

Related questions

113 votes
113 votes
20 answers
1
Sandeep Singh asked Feb 12, 2016
51,647 views
We want to design a synchronous counter that counts the sequence $0-1-0-2-0-3$ and then repeats. The minimum number of $\text{J-K}$ flip-flops required to implement this ...
24 votes
24 votes
7 answers
2
85 votes
85 votes
9 answers
3
Sandeep Singh asked Feb 12, 2016
30,709 views
Consider a carry look ahead adder for adding two $n$-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is$\Theta (1)$$\...