Converting Between Decimal & Binary (AQA GCSE Computer Science)

Revision Note

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James Woodhouse

Written by: James Woodhouse

Reviewed by: Lucy Kirkham

Decimal to Binary Conversion

Decimal to binary conversion

  • It is important to know the process of converting from decimal to binary to understand how computers interpret and process data

Example 1

  • To convert the decimal number 45 to binary, start by writing out the binary headings from right to left

128

64

32

16

8

4

2

1

 

 

 

 

 

 

 

 

  • Start at the leftmost empty column heading (128). Is the decimal number > column heading? (45 > 128) No, put a 0 in the 128 column. Repeat until you put a 1 under a heading. In this example it would be 32

128

64

32

16

8

4

2

1

0

0

1

 

 

 

 

 

  • Next subtract column heading from decimal value, 45-32 = 13

  • Repeat previous two steps until you have a value under each column heading

128

64

32

16

8

4

2

1

0

0

1

0

1

1

0

1

  • 32 + 8 + 4 + 1 = 45

  • Decimal 45 is 00101101 in Binary

Examiner Tips and Tricks

Don't forget to show your working! Data conversion questions will often be worth 2 marks, 1 for the answer and 1 for your working

Example 2

  • To convert the decimal number 213 to binary, start by writing out the binary headings from right to left

128

64

32

16

8

4

2

1

 

 

 

 

 

 

 

 

  • Start at the leftmost empty column heading (128). Is decimal number > column heading? (213 > 128) Yes, put a 1 under the heading.

128

64

32

16

8

4

2

1

1

 

 

 

 

 

 

 

  • Next subtract column heading from decimal value, 213-128 = 85

  • Repeat process until you have a value under each column heading

128

64

32

16

8

4

2

1

1

1

0

1

0

1

0

1

  • 128 + 64 + 16 + 4 + 1 = 213

  • Decimal 213 is 11010101 in Binary

Examiner Tips and Tricks

At GCSE you will only be asked to convert from/to binary up to and including 8 binary digits (8 bits). That means you are working with a decimal range of 0-255 (00000000-11111111)

Binary to Decimal Conversion

Example 1

  • To convert the binary number 1011 to decimal, start by writing out the binary headings from right to left

8

4

2

1

 

 

 

 

  • Write in the binary digits under the headings from left to right

8

4

2

1

1

0

1

1

  • Add together any value with a 1 under it

  • (1 x 8) + (1 x 2) + (1 x 1) = 11

  • Binary 1011 is 11 in Decimal 

Examiner Tips and Tricks

If you are converting from binary to decimal and the binary number ends in 1, the decimal answer must be an odd number!

Example 2

  • To convert the binary number 01100011 to decimal, start by writing out the binary headings from right to left

128

64

32

16

8

4

2

1

 

 

 

 

 

 

 

 

  • Write in the binary digits under the headings from left to right

128

64

32

16

8

4

2

1

0

1

1

0

0

0

1

1

  • Add together any value with a 1 under it

  • (1 x 64) + (1 x 32) + (1 x 2) + (1 x 1) = 99

  • Binary 01100011 is 99 in Decimal

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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.

Lucy Kirkham

Author: Lucy Kirkham

Expertise: Head of STEM

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels.Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all.