Slide 8.2: Overflow

Overflow

Overflow occurs when the result from an operation cannot be represented with the available hardware. When can overflow occur in addition and subtraction?

When adding operands with different signs, overflow can not occur.

When subtracting operands with the same sign, overflow can not occur.

Overflow occurs when adding two positive numbers and the sum is negative, or vice versa.

Overflow occurs in subtraction when we subtract a negative number from a positive number and get a negative result, or when we subtract a positive number from a negative number and get a positive result.

Unsigned integers are commonly used for memory addresses where overflows are ignored.

Add (add), add immediate (addi), and subtract (sub) cause exceptions on overflow.

Add unsigned (addu), add immediate unsigned (addiu), and subtract unsigned (subu) do not cause exceptions on overflow.

add addu (without overflow)

`add`	`addu` (without overflow)
.text li $a0, 2147483647 # largest signed word is # 0x7FFFFFFF = 2³¹-1 # = 2,147,483,647 add $a0, $a0, 1 li $v0, 1 syscall li $v0, 10 syscall	.text li $a0, 2147483647 # largest signed word is # 0x7FFFFFFF = 2³¹-1 # = 2,147,483,647 addu $a0, $a0, 1 li $v0, 1 syscall li $v0, 10 syscall
Output	Output

  .text
  li  $a0, 2147483647

   # largest signed word is
   #   0x7FFFFFFF = 2³¹-1
   # = 2,147,483,647

  add $a0, $a0, 1
  li  $v0, 1
  syscall                 
  li  $v0, 10
  syscall

  .text
  li   $a0, 2147483647

   # largest signed word is
   #   0x7FFFFFFF = 2³¹-1
   # = 2,147,483,647

  addu $a0, $a0, 1
  li   $v0, 1
  syscall                 
  li   $v0, 10
  syscall

Output Output