Binary Addition (Cambridge (CIE) IGCSE Computer Science)

Revision Note

Robert Hampton

Written by: Robert Hampton

Reviewed by: James Woodhouse

Adding Positive 8-bit Binary Integers

What is binary addition?

  • Binary addition is the process of adding together two binary integers (up to and including 8 bits)

  • To be successful there are 5 golden rules to apply:

Binary Addition

Binary Answer

Working

0 + 0 =

0

1s

 

0

= 0

0 + 1 =

1

1s

 

1

= 1

1 + 0 = 

1

1s

 

1

= 1

1 + 1 =

10

2s

1s

 

1

0

= 2

1 + 1 + 1 =

11

2s

1s

 

1

1

= 3

  • Like denary addition, start from the rightmost digit and move left

  • Carrying over occurs when the sum of a column is greater than 1, passing the excess to the next left column

Example 1

  • Add together the binary values 1001 and 0100

8

4

2

1

+

1

0

0

1

0

1

0

0

 

 

 

 

C

 

 

 

 

 

  • Starting from right to left, add the two binary values together applying the 5 golden rules

  • If your answer has 2 digits, place the rightmost digit in the column and carry the remaining digit to the next column on the left

  • In this example, start with 1+0, 1+0 = 1, so place a 1 in the column

8

4

2

1

+

1

0

0

1

0

1

0

0

 

 

 

 

C

 

 

 

1

 

  • Repeat until all columns have a value

8

4

2

1

+

1

0

0

1

0

1

0

0

 

 

 

 

C

1

1

0

1

 

  • The sum of adding together binary 1001 (9) and 0100 (4) is 1101 (13)

Examiner Tips and Tricks

Make sure any carried digits are clearly visible in your answer, there are marks available for working. Carries can be put above or below in the addition

Example 2

  • Add together the binary values 00011001 and 10000100

128

64

32

16

8

4

2

1

+

0

0

0

1

1

0

0

1

1

0

0

0

1

0

0

1

 

 

 

 

 

 

 

 

C

 

 

 

 

 

 

 

 

 

  • Starting from right to left, add the two binary values together applying the 5 golden rules

  • If your answer has 2 digits, place the rightmost digit in the column and carry the remaining digit to the next column on the left

  • In this example, start with 1+1, 1+1 = 10, so place a 0 in the column and carry the 1 to the next column

128

64

32

16

8

4

2

1

+

0

0

0

1

1

0

0

1

1

0

0

0

1

0

0

1

 

 

 

 

 

 

1

 

C

 

 

 

 

 

 

 

0

 

  • Repeat until all columns have a value

128

64

32

16

8

4

2

1

+

0

0

0

1

1

0

0

1

1

0

0

0

1

0

0

1

 

 

1

1

 

 

1

 

C

1

0

1

0

0

0

1

0

 

  • The sum of adding together binary 00011001 (25) and 10001001 (137) is 10100010 (162)

Overflow & Binary Addition

What is an overflow error?

  • An overflow error occurs when the result of a binary addition exceeds the available bits

  • For example, if you took binary 11111111 (255) and tried to add 00000001 (1) this would cause an overflow error as the result would need a 9th bit to represent the answer (256)

256

128

64

32

16

8

4

2

1

+

 

1

1

1

1

1

1

1

1

 

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

 

C

 

0

0

0

0

0

0

0

0

 

Examiner Tips and Tricks

When starting a binary addition question, always look at the question that comes after. If it asks you to name what problem has been caused, you know the binary addition question must cause an overflow error and therefore mean a carried bit that does not fit in to the answer

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Robert Hampton

Author: Robert Hampton

Expertise: Computer Science Content Creator

Rob has over 16 years' experience teaching Computer Science and ICT at KS3 & GCSE levels. Rob has demonstrated strong leadership as Head of Department since 2012 and previously supported teacher development as a Specialist Leader of Education, empowering departments to excel in Computer Science. Beyond his tech expertise, Robert embraces the virtual world as an avid gamer, conquering digital battlefields when he's not coding.

James Woodhouse

Author: James Woodhouse

Expertise: Computer Science

James graduated from the University of Sunderland with a degree in ICT and Computing education. He has over 14 years of experience both teaching and leading in Computer Science, specialising in teaching GCSE and A-level. James has held various leadership roles, including Head of Computer Science and coordinator positions for Key Stage 3 and Key Stage 4. James has a keen interest in networking security and technologies aimed at preventing security breaches.