Adding binary numbers, and overflow Cambridge IGCSE Computer Science (9–1) revision
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In plain words
Binary numbers are added in columns from the right, just like denary, but you carry whenever a column reaches 2.
A register has a fixed number of bits. If the answer is too big to fit, the extra bit has nowhere to go. That is an overflow error.
4 things to know
- The four rules: 0 + 0 = 0. 0 + 1 = 1. 1 + 1 = 0 carry 1. 1 + 1 + 1 = 1 carry 1.
- Work from the right-hand column to the left, writing each carry above the next column.
- An 8-bit register can hold nothing larger than 255. If the sum is more than 255 it needs a ninth bit, and an overflow error occurs.
- Every computer has a limit like this, for example 16 bits. An overflow error happens whenever a result is outside the limit.
Worked example
Add the 8-bit binary numbers 01101011 and 00111010.
- From the right: 1 + 0 = 1. 1 + 1 = 0 carry 1. 0 + 0 + 1 = 1. 1 + 1 = 0 carry 1.
- Carrying on: 0 + 1 + 1 = 0 carry 1. 1 + 1 + 1 = 1 carry 1. 1 + 0 + 1 = 0 carry 1. 0 + 0 + 1 = 1.
- The answer is 10100101.
- Check in denary: 107 + 58 = 165, and 10100101 = 128 + 32 + 4 + 1 = 165.
Tips and tricks
- Show the carries. They earn the working mark even if a later column goes wrong.
- Check your answer by converting all three numbers to denary. It takes a few seconds.
- To explain overflow, give both halves: the result is greater than 255, and so it cannot be stored in 8 bits.
It lands in your notebook with its questions as flashcards.
Adding binary numbers, and overflow: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
In binary, what is 1 + 1?
There is no digit 2 in binary. Write 0 and carry 1.
In binary, what is 1 + 1 + 1?
That is 3 in denary, which is 11: write 1 and carry 1.
What is 00110101 + 00011011?
53 + 27 = 80, and 80 = 64 + 16.
When does an overflow error occur in an 8-bit register?
A result above 255 needs a ninth bit, and there is nowhere to put it.
Which of these 8-bit additions causes an overflow error?
129 + 128 = 257, which is more than 255. The others give 128, 30 and 128.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
2 questions, 5 marks. Write your answers on paper, then check them.
Adding binary numbers, and overflow
Cambridge IGCSE Computer Science (9–1) 0984 · 5 marks · papermunch.org
Name ______________________________ Date ______________
Add the binary numbers 01011001 and 00100110. Give your answer in binary.[2]
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01111111. (89 + 38 = 127. No column produces a carry.)
Add the 8-bit binary numbers 10110110 and 01100001, and explain why the result cannot be stored in an 8-bit register.[3]
Show answerHide answer
100010111. The result (279) is greater than 255, so it needs nine bits. This is an overflow error.
Answers: Adding binary numbers, and overflow
- 1. 01111111. (89 + 38 = 127. No column produces a carry.)
- 2. 100010111. The result (279) is greater than 255, so it needs nine bits. This is an overflow error.