CODEWITHSUNDEEP
c
Charlotte Neuharova
Charlotte Neuharova

Reputation: 1

How does hexadecimal to %x work?

I am learning in C and I got a question regarding this conversion.

short int x = -0x52ea;

printf ( "%x", x );

output:

ffffad16

I would like to know how this conversion works because it's supposed to be on a test and we won't be able to use any compilers. Thank you

Upvotes: 0

Views: 83

Answers (2)

chux
chux

Reputation: 154235

I would like to know how this conversion works

It is undefined behavior (UB)

short int x = -0x52ea;

  1. 0x52ea is a hexadecimal constant. It has the value of 52EA16, or 21,22610. It has type int as it fits in an int, even if int was 16 bit. OP's int is evidently 32-bit.

  2. - negates the value to -21,226.

  3. The value is assigned to a short int which can encode -21,226, so no special issues with assigning this int to a short int.

printf("%x", x );

  1. short int x is passed to a ... function, so goes through the default argument promotions and becomes an int. So an int with the value -21,226 is passed.

  2. "%x" used with printf(), expects an unsigned argument. Since the type passed is not an unsigned (and not an int with a non-negative value - See exception C11dr §6.5.2.2 6), the result is undefined behavior (UB). Apparently the UB on your machine was to print the hex pattern of a 32-bit 2's complement of -21,226 or FFFFAD16.

If the exam result is anything but UB, just smile and nod and realize the curriculum needs updating.

Upvotes: 4

Havenard
Havenard

Reputation: 27894

The point here is that when a number is negative, it's structured in a completely different way.

1 in 16-bit hexadecimal is 0001, -1 is ffff. The most relevant bit (8000) indicates that it's a negative number (admitting it's a signed integer), and that's why it can only go as positive as 32767 (7fff), and as negative as -32768 (8000).

Basically to transform from positive to negative, you invert all bits and sum 1. 0001 inverted is fffe, +1 = ffff.

This is a convention called Two's complement and it's used because it's quite trivial to do arithmetic using bitwise operations when you use it.

Upvotes: 0

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