Question

What is the simples way to check if the sum of two unsigned integers has resulted in an overflow.

Comments

1. If highest bit of both the integers is 1 then definite overflow.
2. If highest bit of both the integers is 0 then definite no overflow.
3. If highest bit of only one then is 1 then may or may not be overflow.

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Extending Salil's Comment

1. If highest bit of both the integers is 1 then definite overflow.
2. If highest bit of both the integers is 0 then definite no overflow.
3. If highest bit of only one then
Assume N1 has most significant bit as 1 and N2 has most significant bit is zero
P1 = first occurrence of 0 in N1 (most significant to least significant)
P2 = first occurrence of 1 in N2

P1 < P2  => will not overflow
P1 > P2 => Will overflow
P1 == P2 => left shift numbers by P1 and repeat from step 1

Answer 1

Try this

int uadd32(uint32 a,uint32 b) {
  unsigned long long x=(unsigned long long) a+b;
  if (x>0xffffffff) return 0; // 0 means overflow
  return 1; // 1 means no overflow
}

Answer 2

May not be fastest solution -
a = b+c
if a is truncated because of overflow the c != a-b

Code

a = b + c;
if (c == (a-b))
    printf("No Overflow");
else
    printf("Overflow");

Comments

Consider this example for 8 bit unsigned integer

a = 255, b = 254
c = a + b = 253
c - a = 254
c - b = 255

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Sorry, I should have tested...(it was a mathematical solution need to code it)