Skip to content
VirtusAcademy

Binary Addition

FoundationHigherAQA

Learn Binary Addition for GCSE Computer Science with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA GCSE Computer Science (8525). Binary numbers are added bit by bit, carrying a 1 whenever the column total reaches two.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA specification. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Binary addition follows four rules, three of which are obvious and one of which is the source of nearly every error.

The rules are: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 — that is, 0 carry 1. Adding three 1s, which happens when a carry arrives, gives 11 — that is, 1 carry 1.

Work from right to left, writing carries above the next column. An overflow occurs when the result needs more bits than are available: adding two 8-bit numbers that total more than 255 produces a ninth bit with nowhere to go. The result stored is then wrong, which is why overflow must be detected rather than ignored.

Revision notes

The four rules

0 + 0 = 0. 0 + 1 = 1. 1 + 0 = 1. 1 + 1 = 0 carry 1.

With a carry already present, 1 + 1 + 1 = 1 carry 1. Work from right to left, writing each carry above the next column.

Working through an addition

Line the numbers up with the rightmost digits aligned.

Add each column including any carry from the previous one. Write the result digit below and the carry above the next column. Continue until every column is done.

Overflow

Overflow occurs when the result requires more bits than are available.

Adding two 8-bit numbers totalling more than 255 produces a ninth bit with nowhere to store it. The stored result is then incorrect, so the system must detect and report the overflow.

Key points

  • 1 + 1 = 0 carry 1 in binary.
  • 1 + 1 + 1 = 1 carry 1.
  • Work from right to left.
  • Write carries above the next column.
  • Overflow needs more bits than available.
  • An overflow makes the stored result wrong.

Worked examples

Example 1

Add the binary numbers 1011 and 0110. [3 marks]

Working

Right column: 1 + 0 = 1. Next: 1 + 1 = 0 carry 1add the first two columns
Next: 0 + 1 + carry 1 = 0 carry 1. Next: 1 + 0 + carry 1 = 0 carry 1add the remaining columns with carries
The carry gives a fifth bit, so the answer is 10001include the final carry

Example 2

Explain what overflow means in binary addition. [2 marks]

Working

The result of the addition requires more bits than are available to store itstate what happens
so the extra bit is lost and the stored result is incorrectexplain the consequence

Example 3

State the result of adding 1 + 1 + 1 in binary. [2 marks]

Working

1 + 1 + 1 = 3 in denary, which is 11 in binaryconvert the sum to binary
so the column result is 1 with a carry of 1state the digit and carry

Common mistakes

  • Writing 1 + 1 = 2 in binary.

    There is no digit 2 — it is 0 carry 1.

  • Forgetting to include the carry.

    Each column must add any carry from the previous one.

  • Dropping the final carry.

    It becomes an extra bit at the left of the answer.

  • Ignoring overflow.

    It means the stored result is wrong and must be reported.

Exam tips

  • Write carries clearly above the next column.
  • Work right to left without skipping.
  • Include the final carry in the answer.
  • Check for overflow if the bit count is fixed.

Key terms

Carry
A bit passed to the next column when a sum exceeds 1.
Overflow
A result needing more bits than are available.
Binary addition
Adding numbers in base 2.
Most significant bit
The leftmost bit of a binary number.

Related topics

Written and reviewed against the current AQA specification. Spotted an error? Let us know.