What is the difference between (unsigned)~0 and (unsigned)1. Why is unsigned of ~0 is -1 and unsigned of 1 is 1? Does it have something to do with the way unsigned numbers are stored in the memory. Why does an unsigned number give a signed result. It didn't give any overflow error either. I am using GCC compiler:
#include<sdio.h>
main()
{
unsigned int x=(unsigned)~0;
unsigned int y=(unsigned)1;
printf("%d\n",x); //prints -1
printf("%d\n",y); //prints 1
}
Because %d is a signed int specifier. Use %u.
which prints 4294967295 on my machine.
As others mentioned, if you interpret the highest unsigned value as signed, you get -1, see the wikipedia entry for two's complement.
Your system uses two's complement representation of negative numbers. In this representation a binary number composed of all ones represent the biggest negative number -1.
Since inverting all bits of a zero gives you a number composed of all ones, you get -1 when you re-interpret the number as a signed number by printing it with a %d which expects a signed number, not an unsigned one.
First, in your use of printf you are telling it to print the number as signed ("%d") instead of unsigned ("%u").
Second, you are right in that it has "something to do with the way numbers are stored in memory". An int (signed or unsigned) is not a single bit on your computer, but a collection of k bits. The exact value of k depends on the specifics of your computer architecture, but most likely you have k=32.
For the sake of succinctness, lets assume your ints are 8 bits long, so k=8 (this is most certainly not the case, unless you are working on a very limited embedded system,). In that case (int)0 is actually 00000000, and (int)~0 (which negates all the bits) is 11111111.
Finally, in two's complement (which is the most common binary representation of signed numbers), 11111111 is actually -1. See http://en.wikipedia.org/wiki/Two's_complement for a description of two's complement.
If you changed your print to use "%u", then it will print a positive integer that represents (2^k-1) where k is the number of bits in an integer (so probably it will print 4294967295).
printf() only knows what type of variable you passed it by what format specifiers you used in your format string. So what's happening here is that you're printing x and y as signed integers, because you used %d in your format string. Try %u instead, and you'll get a result more in line with what you're probably expecting.
Related
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
I would like to know how this conversion works
It is undefined behavior (UB)
short int x = -0x52ea;
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.
- negates the value to -21,226.
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 );
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.
"%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 ยง6.5.2.2 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.
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.
Here is a code snippet:
unsigned short a=-1;
unsigned char b=-1;
char c=-1;
unsigned int x=-1;
printf("%d %d %d %d",a,b,c,x);
Hhy the output is this:
65535 255 -1 -1
?
Can anybody please analyze this ?
You are printing the values using %d which is for signed numbers. The value is "converted" to a signed number (it actually stays the same bitwise, but the first bit is interpreted differently).
As for unsigned char and short - they are also converted to 32 bit int, so the values fit in it.
Had you used %lld (and cast the value as long long, otherwise it could be unspecified behavior) even the last two numbers may get printed as unsigned.
Anyway, use %u for unsigned numbers.
How does it work?
Bit value of 255 is 11111111. If treated like an unsigned number, it will be 255. If treated as a signed number - it'll be -1 (the first bit usually determines sign).
When you pass the value to %d in printf, the value is converted to a 32 bit integer, which looks like this: 00000000000000000000000011111111. Since the first bit is 0, the value is printed simply as 255. It works similarily for your short.
The situation is different for 32 bit integer. It is immediately assigned a 11111111111111111111111111111111 value, which stands for -1 in singed notation. And since you have used %d in your printf, it is interpreted as -1.
Basically, you should not assign negative values to "unsigned" variables. You are trying to play tricks on the compiler, and who knows what it will do. Now, "char n = -1;" is OK because "n" can legitimently take on negative values and the compiler knows how to treat it.
In the C programming language, unsigned int is used to store positive values only. However, when I run the following code:
unsigned int x = -12;
printf("%d", x);
The output is still -12. I thought it should have printed out: 12, or am I misunderstanding something?
The -12 to the right of your equals sign is set up as a signed integer (probably 32 bits in size) and will have the hexadecimal value 0xFFFFFFF4. The compiler generates code to move this signed integer into your unsigned integer x which is also a 32 bit entity. The compiler assumes you only have a positive value to the right of the equals sign so it simply moves all 32 bits into x. x now has the value 0xFFFFFFF4 which is 4294967284 if interpreted as a positive number. But the printf format of %d says the 32 bits are to be interpreted as a signed integer so you get -12. If you had used %u it would have printed as 4294967284.
In either case you don't get what you expected since C language "trusts" the writer of code to only ask for "sensible" things. This is common in C. If you wanted to assign a value to x and were not sure whether the value on the right side of the equals was positive you could have written unsigned int x = abs(-12); and forced the compiler to generate code to take the absolute value of a signed integer before moving it to the unsigned integer.
The int is unsinged, but you've told printf to look at it as a signed int.
Try
unsigned int x = -12; printf("%u", x);
It won't print "12", but will print the max value of an unsigned int minus 11.
Exercise to the reader is to find out why :)
Passing %d to printf tells printf to treat the argument as a signed integer, regardless of what you actually pass. Use %u to print as unsigned.
It all has to do with interpretation of the value.
If you assume 16 bit signed and unsigned integers, then here some examples that aren't exactly correct, but demonstrate the concept.
0000 0000 0000 1100 unsigned int, and signed int value 12
1000 0000 0000 1100 signed int value -12, and a large unsigned integer.
For signed integers, the bit on the left is the sign bit.
0 = positive
1 = negative
For unsigned integers, there is no sign bit.
the left hand bit, lets you store a larger number instead.
So the reason you are not seeing what you are expecting is that.
unsigned int x = -12, takes -12 as an integer, and stores it into x. x is unsigned, so
what was a sign bit, is now a piece of the value.
printf lets you tell the compiler how you want a value to be displayed.
%d means display it as if it were a signed int.
%u means display it as if it were an unsigned int.
c lets you do this kind of stuff. You the programmer are in control.
Kind of like a firearm.
It's a tool.
You can use it correctly to deal with certain situations,
or incorrectly to remove one of your toes.
one possibly useful case is the following
unsigned int allBitsOn = -1;
That particular value sets all of the bits to 1
1111 1111 1111 1111
that can be useful sometimes.
printf('%d', x);
Means print a signed integer. You'll have to write this instead:
printf('%u', x);
Also, it'll still not print "12", it's going to be "4294967284".
They do store positive values. But you're outputting the (very high) positive value as a signed integer, so it gets re-interpreted again (in an implementation-defined fashion, I might add).
Use the format flag "%u instead.
Your program has undefined behavior because you passed the wrong type to printf (you told it you were going to pass an int but you passed an unsigned int). Consider yourself lucky that the "easiest" thing for the implementation to do was just silently print the wrong value and not jump to some code that does something harmful...
What you are missing is that the printf("%d",x) expects x to be signed, so although you assign -12 to x it is interpreted as 2's complement which would be a very large number.
However when you pass this really large number to printf it interprets it as signed thus correctly translating it back to -12.
The correct syntax to print a unsigned in print f is "%u" - try this and see what it does!
The assignment of a negative value to an unsigned int does not compute the absolute value of the negative: it interprets as an unsigned int the binary representation of the negative value, i.e., 4294967284 (2^32 - 12).
printf("%d") performs the opposite interpretation. This is why your program displays -12.
int and unsigned int are used to allocate a number of bytes to store a value nothing more.
The compiler should give warnings about signed mismatching but it really does not affect the bits in the memory that represent the value -12.
%x, %d, %u etc tells the compiler how to interrupt a number of bits when you print them.
When you are trying to display the int value you are passing it to a (int) argument and not a (unsigned int) argument and that causes it to print -12 and not 4294967284. Integers are stored in hexadecimal format and -12 for int is the same as 4294967284 for unsigned int in hexadecimal format..
That is why "%u" prints the right value you want and not "%d".. It depends on your argument type..GOOD LUCK!
The -12 is in 16-bit 2's compliment format. So do this:
if (x & 0x8000) { x = ~x+1; }
This will convert the 2's compliment -ve number to the equivalent +ve number. Good luck.
When the compiler implicitly converts -12 to an unsigned integer, the underlying binary representation remains unaltered. This conversion is purely semantic. The sign bit of the two's complement integer becomes the most significant bit of the unsigned integer. Thus when printf treats the unsigned integer as a signed integer with %d, it will see -12.
In general context when only positive numbers can be stored, negative numbers are not stored explicitly but their 2's complement is stored. In the same way here, the 2's complement of -12 will be stored in 'x' and you use %u to get it.
Please explain the following paragraph.
"The next question is whether we can assign a certain value to a variable without losing precision. It is not sufficient if we just check for overflow during the addition or subtraction, because someone might add 1 to -5 and assign the result to an unsigned int. Then the actual addition does not overflow, but the result still does not fit."
when i am adding 1 to -5 i dont see any reason to worry.the answer is as it should be -4.
so what is the problem of result not being fit??
you can find the full article here through which i was going:
http://www.fefe.de/intof.html
The binary representation of -4, in a 32-bit word, is as follows (hex notation)
0xfffffffc
When interpreted as an unsigned integer, this bit pattern represents the number 2**32-4, or 18446744073709551612. I'm not sure I would call this phenomenon "overflow", but it is a common mistake to assign a small negative integer to a variable of unsigned type and wind up with a really big positive integer.
This trick is actually exploited for bounds checking: if you have a signed integer i and want to know if it is in the range 0 <= i < n, you can test
if ((unsigned)i < n) { ... }
which gives you the answer using one comparison instead of two. The cast to unsigned has no run-time cost; it just tells the compiler to generate an unsigned comparison instead of a signed comparison.
Try assigning it to a unsigned int, not an int.
The term unsigned int is the key - by default an int datatype will hold negative and positive numbers; however, unsigned ints are always positive. They provide this option because uints can technically hold greater positive values than regular signed ints because they do not need to use a bit to keep track of whether or not its negative or positive.
Please see:
Signed versus Unsigned Integers
The problem is that you're storing -4 in an unsigned int. Unsigned ints can only contain zero and positive values. If you assign -4 to one, you'll actually end up getting a very large positive number (the actual value depends on how wide an int you're using).
The problem is that the sizes of storage such as unsigned int can only hold so much. With 1 and -5 it does not matter, but with 1 and -500000000 you might end up with a confusing result. Also, unsigned storage will interpret anything stored in it as positive, so you cannot put a negative value in an unsigned variable.
Two big things to watch out for:
1. Overflow in the operation itself: 1 + -500000000
2. Issues in casting: (unsigned int)(1 + -500)
Unsigned variables, like unsigned int, cannot hold negative values. So assigning 1 - 5 to an unsigned int won't give you -4. I'm not sure what it'll give you, it's probably compiler specific.
Some code:
signed int first, second;
unsigned int result;
first = obtain(); // happens to be 1
second = obtain(); // happens to be -5
result = first + second; // unexpected result here - very large number - and it's too late to check that there's a problem
Say you obtained those values from keyboard. You need to check before addition that the result can be represented in unsigned int. That's what the article talks about.
By definition the number -4 cannot be represented in an unsigned int. -4 is a signed integer. The same goes for any negative number.
When you assign a negative integer to an unsigned int the actual bits of the number do not change, but they are merely represented differently. You'll get some ridiculously-large number due to the way integers are represented in binary (two's complement).
In two's complement, -4 is represented as 0xfffffffc. When 0xfffffffc is represented as an unsigned int you'll get the number 4,294,967,292.
You have to remember that fundamentally you're working with bits. So you can assign a value of -4 to an unsigned integer and this will place a series of bits into that memory location. Those bits can be interpreted as -4 in certain circumstances. One such circumstance is the obvious one: you've told the compiler/system that the bits in that memory location should be interpreted as a two's compliment signed number. So if you do printf("%s",i) prtinf does its magic and converts the two's compliment number to a magnitude and sign. The magnitude will be 4 and the sign will be negative, so it displays '-4'.
However, if you tell the compiler that the data at that memory location is not signed then the bits don't change but instead their interpretation does. So when you do your addition, store the result in an unsigned integer memory location and then call printf on the result it doesn't bother looking for the sign because by definition it is always positive. It calculates the magnitude and prints it. The magnitude will be off because the sign information is still encoded in the bits but it's treated as magnitude information.
I'm reading the second edition of K&R book and one of the exercises requires printing all maximum integer values defined in limits.h header. However, this...
printf("unsigned int: 0 to %d\n", UINT_MAX);
... outputs the following:
unsigned int: 0 to -1
How come I get -1? Anyone could explain this behaviour?
I'm using Digital Mars C compiler on Vista.
This is because UINT_MAX resolves to -1 if treated as a signed integer. The reason for this is, that integers are represented in two's-complement. As a consequence, -1 and 4294967296 (i.e. UINT_MAX) have the same bit representation (0xFFFFFFFF, i.e. all bits set) and that's why you get a -1 here.
Update:
If you use "%u" as the format string you will get the expected result.
In the printf, I believe %d is a signed decimal integer, try %u instead.
The max value of an unsigned int has the most significant bit set (it is all 1s). With a signed int, the most significant bit specifies negative numbers, so when you're printing an unsigned int as a signed int, printf thinks it is negative.