Question

int a = -534;
unsigned int b = (unsigned int)a;
printf("%d, %d", a, b);

prints -534, -534

Why is the typecast not taking place?

I expected it to be -534, 534

---

If I modify the code to

int a = -534;
unsigned int b = (unsigned int)a;
if(a < b)
  printf("%d, %d", a, b);

its not printing anything… after all a is less than b??

Answer 1

First, you don’t need the cast: the value of a is implicitly converted to unsigned int with the assignment to b. So your statement is equivalent to:

unsigned int b = a;

Now, an important property of unsigned integral types in C and C++ is that their values are always in the range [0, max], where max for unsigned int is UINT_MAX (it’s defined in limits.h). If you assign a value that’s not in that range, it is converted to that range. So, if the value is negative, you add UINT_MAX+1 repeatedly to make it in the range [0, UINT_MAX]. For your code above, it is as if we wrote: unsigned int b = (UINT_MAX + a) + 1. This is not equal to -a (534).

Note that the above is true whether the underlying representation is in two’s complement, ones’ complement, or sign-magnitude (or any other exotic encoding). One can see that with something like:

signed char c = -1;
unsigned int u = c;
printf("%u\n", u);
assert(u == UINT_MAX);

On a typical two’s complement machine with a 4-byte int, c is 0xff, and u is 0xffffffff. The compiler has to make sure that when value -1 is assigned to u, it is converted to a value equal to UINT_MAX.

Now going back to your code, the printf format string is wrong for b. You should use %u. When you do, you will find that it prints the value of UINT_MAX - 534 + 1 instead of 534.

When used in the comparison operator <, since b is unsigned int, a is also converted to unsigned int. This, given with b = a; earlier, means that a < b is false: a as an unsigned int is equal to b.

Let’s say you have a ones’ complement machine, and you do:

signed char c = -1;
unsigned char uc = c;

Let’s say a char (signed or unsigned) is 8-bits on that machine. Then c and uc will store the following values and bit-patterns:

+----+------+-----------+
| c  |  -1  | 11111110  |
+----+------+-----------+
| uc | 255  | 11111111  |
+----+------+-----------+

Note that the bit patterns of c and uc are not the same. The compiler must make sure that c has the value -1, and uc has the value UCHAR_MAX, which is 255 on this machine.

There are more details on my answer to a question here on SO.