Binary Addition & Overflow Error
Binary Addition Rules
- 0+0=0
- 1+0=1
- 0+1=1
- 1+1=0 (carry 1)
- 1+1+1=1 (carry 1)
- Write numbers in columns, LSB to MSB.
- Apply rules row by row, moving left.
- Record any carry above the next column.
- Keep result to required bit-length (e.g.
a byte = 8 bits).
Checking Answers
- Convert each operand and result back to denary.
- Ensure \text{denary A}+\text{denary B}=\text{denary result}.
Overflow Error
- Occurs when the calculated value needs more bits than the field allows.
- Typical byte limit: max 111111112 = 255{10}.
- Extra carry beyond MSB is lost ⇒ wrong stored value.
- Example: 10010111 + 10000001 = 00011000 in 8 bits; true answer needs 9 bits, so overflow.
Key Terms
- Binary
- Carry bit
- Overflow error
- 8-bit / byte