Question

The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is________.

Answer 1

16- bit 2’s complement representation of an integer is:

an interval gives the probability that the value of the variable lies within the same interval. To convert this into decimal form:

1)  First take the 1’s complement of it:

1111 1111 1111 0101 => 0000 0000 0000 1010

2) Now add 1 to it:

0000 0000 0000 1010 + 1 = 0000 0000 0000 1011

3) Now, all 0’s in left side have no meaning in decimal form. Just take the number 1011

4) As, 1011 decimal representation is 11. But here sign bit is 1, means it is a negative number.

5) if MSB = 0, number is positive and if MSB = 1 , number is negative.

6) So, result is – 11.

Alternate Method:

1111 1111 1111 0101 ≡ 10101

10101 = 1 × 2^-4 + 0 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰ = -16 + 4 + 1 = -11