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 $1$)

Performing Binary Addition (Method)

• 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 $11111111<em>2 = 255</em>{10}$.
• 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