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

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

1.2.4a Data Storage: Numbers

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Data Storage: Numbers — Note 2 of 5

What you need to know

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.

What to know

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).

Key terms

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 technique

Tip:When doing binary addition, work from RIGHT to LEFT (least significant bit first), just like denary addition.
Mistake:Forgetting to carry. Always check each column carefully and note any carry digits clearly.
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.
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.
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.

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