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

Revision Note

Robert Hampton

Written by: Robert Hampton

Reviewed by: James Woodhouse

Binary to Hexadecimal Conversion

How do you convert from binary to hexadecimal?

  • It is important before revising how to convert from binary to hexadecimal and vice versa that you fully understand the binary and hexadecimal number systems.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

Example 1

  • To convert the binary number 10110111 to hexadecimal, first split the 8 bit number into 2 binary nibbles

8

4

2

1

 

 

8

4

2

1

1

0

1

1

0

1

1

1

  • For each nibble, convert the binary to it’s denary value

  • (1 x 8) + (1 x 2) + (1 x 1) = 11 (B)

  • (1 x 4) + (1 x 2) + (1 x 1) = 7

  • Join them together to make a 2 digit hexadecimal number

  • Binary 10110111 is B7 in hexadecimal

Example 2

  • To convert the binary number 00111001 to hexadecimal, first split the 8 bit number into 2 binary nibbles

8

4

2

1

 

 

8

4

2

1

0

0

1

1

1

0

0

1

  • For each nibble, convert the binary to it’s denary value

  • (1 x 2) + (1 x 1) = 3

  • (1 x 8) + (1 x 1) = 9

  • Join them together to make a 2 digit hexadecimal number

  • Binary 00111001 is 39 in hexadecimal

Hexadecimal to Binary Conversion

How do you convert from hexadecimal to binary?

Example 1

  • To convert the hexadecimal number 5F to binary, first split the digits apart and convert each to a binary nibble

8

4

2

1

 

0

1

0

1

= 5

8

4

2

1

 

1

1

1

1

= 15 (F)

  • Join the 2 binary nibbles together to create an 8 bit binary number

128

64

32

16

8

4

2

1

0

1

0

1

1

1

1

1

  • Hexadecimal 5F is 01011111 in binary

Example 2

  • To convert the hexadecimal number 26 to binary, first split the digits apart and convert each to a binary nibble

8

4

2

1

 

0

0

1

0

= 2

8

4

2

1

 

0

1

1

0

= 6

  • Join the 2 binary nibbles together to create an 8 bit binary number

128

64

32

16

8

4

2

1

0

0

1

0

0

1

1

0

  • Hexadecimal 26 is 00100110 in binary

Last updated:

You've read 0 of your 5 free revision notes this week

Sign up now. 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.