16 位 -32768 到 32767 与 32 位与 64 位的范围 Integer -2147483648 到 2147483647

Question

I've seen lots of places say:

In Turbo c and 16-bit range of Integer is -32768 to 32767 (0 to 65535) but in 32-bit and 64-bit range of Integer is -2147483648 [minimum value -2^31] to 2147483647 [maximum value 2^31-1] . But when we code and try to overflow the integer range like x=2147483649 c compiler returned x=-2147483647.

When we give (+ve) overflow value in x variable it returns (-ve) value or vise versa. And when we enter (+/-ve)2147483648 it always give (-ve) 2147483648 WHY ??

Example Code for better explanation

#include<stdio.h>

int main(){

    int x;

    x=2147483649;

    printf("%d",x);
    
    // if we give x=2147483649
    // Output will be -2147483647

    // if we give x=-2147483649
    // output will be +2147483647

    // if we give x=(+/-)2147483648
    // output will ve always -ve 2147483648

    return 0;

}

Answer 1

In an assignment such as x = 2147483649 , the value on the right is converted to the type of the left operand. When converting to a signed integer type, if the source value cannot be represented in the destination type, the result of the conversion is defined by the implementation (largely by the compiler), per C 2018 6.3.1.3 3.

GCC defines the conversion to wrap modulo 2 ^N , where N is the number of bits in the type ¹ , and this is a common behavior among compilers.

Wrapping 2,147,483,649 modulo 2 ³² produces 2,147,483,649 − 4,294,967,296 = −2,147,483,647.

This is not an overflow. Overflow, or, more generally, an exceptional condition , occurs when the result of an operation is not representable in the result type of the operation (C 2018 6.5 5). Since the conversion is defined to produce a result that is representable, no overflow occurs.

Footnote

¹ The number of value bits and the sign bit, so 32 in this case. Padding bits are not included.

Answer 2

It helps if you look at the bit patterns of all those numbers. 32 bits is 8 hex digits, anything longer than that gets truncated on the left:

               32 bit       64 bit
2147483649:  0x80000001  0x0000000080000001
-2147483647: 0x80000001  0xffffffff80000001
-2147483649: 0x7fffffff  0xffffffff7fffffff
2147483647:  0x7fffffff  0x000000007fffffff
2147483648:  0x80000000  0x0000000080000000
-2147483648: 0x80000000  0xffffffff80000000