Converting Between Binary & Denary (Cambridge (CIE) IGCSE Computer Science)

Revision Note

Robert Hampton

Written by: Robert Hampton

Reviewed by: James Woodhouse

Denary to Binary Conversion

How do you convert denary to binary?

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

  • To convert from denary to binary you must start by writing out a binary number line

  • Find the first column heading with a value larger than the denary value you are converting

  • Write down each column heading to the right (not including the largest heading) until you reach 1

32,768

16,384

8,192

4,096

2,048

1,024

512

256

128

64

32

16

8

4

2

1

Example 1

  • To convert the denary number 45 to binary, start by writing out the binary number line

  • The first column heading larger than 45 is 64, so the number line would be:

32

16

8

4

2

1

 

 

 

 

 

 

  • Start at the leftmost empty column heading (32)

  • Divide column heading into denary number (how many times does 32 fit into 45?)

    • 1 time with 13 remaining

13

32

16

8

4

2

1

 1

 

 

 

 

 

  • Repeat with next column heading (how many times does 16 fit into 13?)

    • 0 times with 13 remaining

13

13

32

16

8

4

2

1

1

0

  • Repeat until all columns have a binary value

13

13

5

1

1

0

32

16

8

4

2

1

1

0

1

1

0

1

  • Denary 45 is 101101 in binary (6 bits)

Examiner Tips and Tricks

Always read the question carefully to check for how many bits are expected in your answer

  • In the example above, a 6 bit answer has been given

  • If they question requires an 8 bit answer, add 2 extra 0s to the start of the answer

  • Denary 45 is 101101 in 6 bit binary and 00101101 in 8 bit binary

Example 2

  • To convert the denary number 3059 to binary, start by writing out the binary number line

  • The first column heading larger than 3059 is 4096, so the number line would be:

2,048

1,024

512

256

128

64

32

16

8

4

2

1

  • Start at the leftmost empty column heading (2048)

  • Divide column heading into denary number (how many times does 2048 fit into 3059?)

    • 1 time with 1011 remaining

1011

2,048

1,024

512

256

128

64

32

16

8

4

2

1

1

  • Repeat with next column heading (how many times does 1024 fit into 1011?)

    • 0 times with 1011 remaining

1011

1011

2,048

1,024

512

256

128

64

32

16

8

4

2

1

1

0

  • Repeat until all columns have a binary value

1011

1011

499

243

115

51

19

3

3

3

1

0

2,048

1,024

512

256

128

64

32

16

8

4

2

1

1

0

1

1

1

1

1

1

0

0

1

1

  • Denary 3059 is 101111110011 in binary (12 bits)

Binary to Denary Conversion

  • To convert from binary to denary, count how many bits make up the value

  • Write out the column headings for the number of bits given from right to left

  • Add together any column heading with a value of 1 in the column

Example 1 (4 bits)

  • To convert the binary number 1011 to denary, 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 column heading with a 1 under it

  • (1 x 8) + (1 x 2) + (1 x 1) = 11

  • Binary 1011 is 11 in denary 

Examiner Tips and Tricks

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

Example 2 (8 bits)

  • To convert the binary number 01100011 to denary, 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 column heading with a 1 under it

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

  • Binary 01100011 is 99 in denary 

Example 3 (14 bits)

  • To convert the binary number 01110001110100 to denary, start by writing out the binary headings from right to left

8,192

4,096

2,048

1,024

512

256

128

64

32

16

8

4

2

1

0

1

1

1

0

0

0

1

1

1

0

1

0

0

  • Add together any column heading with a 1 under it

  • (1 x 4096) + (1 x 2048) + (1 x 1024) + (1 x 64) + (1 x 32) + (1 x 16) + (1 x 4) = 7284

  • Binary 01110001110100 is 7284 in denary 

Last updated:

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

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.