16-bit two's complement number

Question

The question is
What are two's complement numbers of the following 16-bit numbers?

1.0x3f9d

My answer is:

0011111110011101 in binary because 0x3f9d is a positive number.

However, some people said that the answer is:

1100000001100011

I am confusing because 1100000001100011 is a negative number. Which one is the right answer?

0011111110011101 is correct.What's this got to do with C though? — DeiDei
If the input is positive, the result of negation is surely negative. (though the reverse is not necessarily true) — harold

Lundin Lundin · Accepted Answer · 2016-11-04T12:31:54

3F9Dh is a positive number, equal to 0011 1111 1001 1101 binary. It only makes sense to speak of two's complement when a number is negative.

You might be confusing the term two's complement presentation (of a number) with the algorithm "calculate two's complement of x". If you would calculate the two's complement of 3F9Dh, you would indeed end up with 1100 0000 0110 0011.

In C you could do this calculation as

(uint16_t)~0x3F9D + 1

which is equivalent to

(uint16_t)-0x3F9D

(assuming two's complement CPU and not some exotic nonsense CPU)

16-bit two's complement number

1 Answers