CODEWITHSUNDEEP
cnumbersintoverflow
Thor
Thor

Reputation: 10068

Range of 32 bit unit C programming language

I'm currently studying C programming language by following the book "C primer plus".

In the section on overflow, the author states

minimum range for long is –2,147,483,647 to 2,147,483,647, corresponding to a 32-bit unit.

I was wondering, shouldn't the max value for a 32 bit unit be 2,147,483,648 and not 2,147,483,647 as stated by the author?

I have also seen on tutorial point that the range for a 32 bit unit is –2,147,483,648 to 2,147,483,647. I'm extremely confused.

Also, when I run the code 

int i = 2147483647;
printf("%d %d %d\n", i, i+1, i+2);

I got the result 2147483647 -2147483648 -2147483647, which support that the range of 32 bit unit is –2,147,483,648 to 2,147,483,647. So which one is correct?

PS - I have studied two's complement system previous, and from what I can remember, the max number should always be the -(min number) + 1, so from the two's complement system, I was thinking that –2,147,483,647 to 2,147,483,648 is more likely to be correct. But the printf above seem to support –2,147,483,648 to 2,147,483,647, and both are different to what the author stated –2,147,483,647 to 2,147,483,647.

Upvotes: 3

Views: 914

Answers (2)

John Fischer III
John Fischer III

Reputation: 11

–2,147,483,648 to 2,147,483,647 plus ZERO. Simply put, you forgot to count the ZERO.

Upvotes: 0

chux
chux

Reputation: 154592

32-bits of memory can encode, at most, 232 different values.

C integers consists of 3 parts: sign bit, values bits and rarely padding bits. For this answer, assume the number of padding bits is zero.

C supports 3 integer encodings: 2's complement, 1's complement, sign magnitude.

A 32-bit integer then has the range of

  1. 2's complement: [–2,147,483,648 ... 2,147,483,647] Most common by far
  2. 1's complement: [–2,147,483,647 ... 2,147,483,647] 1 smaller range than 2's
  3. sign magnitude: [–2,147,483,647 ... 2,147,483,647] 1 smaller range than 2's

All 3 then meet the C requirement for a long:

Their implementation-defined values shall be equal or greater in magnitude (absolute value) to those shown, with the same sign.
- minimum value for an object of type long int LONG_MIN -2147483647
- maximum value for an object of type long int LONG_MAX +2147483647 C11dr §5.2.4.2.1 1

Note that long as well as int could be 64-bit and have a much wider range.

I was wondering, shouldn't the max value for a 32 bit unit be 2,147,483,648

2,147,483,648 is not compatible with a 32-bit 2's complement as that would take 33 bits.

Avoid integer overflow in C as it is undefined behavior (UB). OP's text output is not definitive.

int i = 2147483647;   // v----v----- UB
printf("%d %d %d\n", i, i+1, i+2);

Instead print the min/max based on <limits.h>:

printf("int  min:%d max:%d\n", INT_MIN, INT_MAX);
printf("long min:%ld max:%ld\n", LONG_MIN, LONG_MAX);

Even if OP's minimum integer is –2,147,483,648, that does not mean that it is the minimum value on all implementations. The C spec only requires –2,147,483,647 or less.

Upvotes: 3

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