Overflow and underflow

Overview

What happens when a result will not fit the word length, how overflow shows itself when two positives or two negatives are added, and where underflow arises in floating point.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Define overflow.

   Model answer

   Overflow occurs when the result of a calculation is too large for the number of bits allocated. The stored answer is then wrong, because the leading bits have nowhere to go.

2. 2

   Define underflow.

   Model answer

   Underflow occurs when a result is too small in magnitude to be represented. The value is usually stored as zero, losing the information it carried.

3. 3

   How does overflow show itself when adding two positive two's complement numbers?

   Model answer

   Two positive numbers that add to a negative answer signal overflow. The sum of 01111111 and 00000001 is 10000000, which reads as −128.

4. 4

   How does overflow show itself when adding two negative two's complement numbers?

   Model answer

   Two negative numbers that add to a positive answer signal overflow. The sum of 10000000 and 11111111 is 01111111, which reads as +127 instead of −129.

5. 5

   State the rule a processor uses to detect two's complement overflow.

   Model answer

   Overflow is flagged when the carry into the sign column differs from the carry out of it. Matching carries mean the answer is valid.

6. 6

   What happens when 11111111 and 00000001 are added in an unsigned 8-bit register?

   Model answer

   The eight stored bits become 00000000 and a carry of 1 leaves the register. Denary 255 plus 1 should be 256, which needs nine bits.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.