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Binary Addition

Computer Science: Edexcel IGCSE, topic 3.1.3

Binary Addition

We can add two binary numbers in exactly the same way as denary numbers.

Adding two digits

Adding two digits

  • If we add 0 + 0 we get 0.
  • If we add 1 + 0 (or 0 + 1) we get 1.
  • If we add 1 + 1, then we cannot use the symbol 2. So we need to carry the 1 and put 0 in the current place.
Adding in a third bit

Adding in a third bit

  • It might be the case that we have 1 + 1 and also a 1 carried over from the previous column.
  • If this is the case, then we carry the 1 and have 1 left over.
  • So we carry 1 and put 1 in the current place.
Overflow errors

Overflow errors

  • Binary numbers are stored as a fixed length.
  • If a number is carried past the last place column, then this is called an overflow error.
  • Overflow errors can lead to inaccurate results and software crashes.

Test yourself on Binary Addition

  • What is overflow?

  • What is the result of adding the binary numbers 1011 and 0101?

  • Why is a carry used in binary addition?

  • What happens when a binary addition results in a number that exceeds the available bit length?

  • Which of the following binary additions will cause an overflow error in an 8-bit system?

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