Numbers: How to add two binary integers together (up to and including 8 bits) and explain overflow errors which may occur

Binary addition follows simple rules. When the result exceeds the number of bits available (e.g. 9 bits in an 8-bit system), an overflow error occurs and the result is incorrect.

Key points

• Binary addition rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1).
• When adding 1+1+1 (with a carry): result is 11 (write 1, carry 1).
• Definition:Overflow Error: occurs when the result of a binary calculation requires more bits than are available. The extra bit is lost, making the result incorrect.
• Exam Tip:When doing binary addition, work from RIGHT to LEFT (least significant bit first), just like denary addition.
• Common Mistake:Forgetting to carry. Always check each column carefully and note any carry digits clearly.
• Exam Tip:If a question asks you to add two 8-bit numbers and the result needs 9 bits, state that an OVERFLOW ERROR has occurred.
• Exam Tip:You MUST show your working (carries) to get the working mark. Converting to denary, adding, then converting back does NOT get the working mark — only the answer mark.
• Exam Tip:Write clearly — if you need to change a 1 to a 0, cross out clearly and write the new digit separately. Overwriting can make your answer illegible.