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

Revision Note

Robert Hampton

Written by: Robert Hampton

Reviewed by: James Woodhouse

Denary to Hexadecimal Conversion

How do you convert denary to hexadecimal?

Method 1 (denary to binary to hexadecimal) 

128

64

32

16

8

4

2

1

0

0

0

1

1

1

0

0

  • Split the 8 bit binary number into two nibbles as shown below

8

4

2

1

 

 

8

4

2

1

0

0

0

1

1

1

0

0

  • Convert each nibble to its denary value

  • 0001 = 1 and 1100 = 12

  • Using the comparison table, the denary value 1 is also 1 in hexadecimal whereas denary value 12 is represented in hexadecimal as C

  • Denary 28 is 1C in hexadecimal

Method 2 (divide by 16)

  • To convert the denary number 163 to hexadecimal, start by dividing the denary value by 16 and recording the whole times the number goes in and the remainder

  • 163 ➗16 = 10 remainder 3

  • In hexadecimal the whole number = digit 1 and the remainder = digit 2

  • Digit 1 = 10 (A)

  • Digit 2 = 3

  • Denary 163 is A3 in hexadecimal

Hexadecimal to Denary Conversion

How do you convert hexadecimal to denary?

Method 1 (hexadecimal to binary to denary)

  • To convert the hexadecimal number B9 to denary, take each hexadecimal digit and convert it from its denary value to 4 bit binary (nibble)

B (11)

 

 

 

9

8

4

2

1

8

4

2

1

1

0

1

1

1

0

0

1

  • Join the two nibbles to make an 8 bit number (byte)

  • Convert from binary to denary

128

64

32

16

8

4

2

1

1

0

1

1

1

0

0

1

  • (1 x 128) + (1 x 32) + (1 x 16) + (1 x 8) + (1 x 1) = 185

  • Hexadecimal B9 is 185 in denary

Method 2 (multiply by 16)

  • To convert the hexadecimal number 79 to denary, start by multiplying the first hexadecimal digit by 16

  • 7 ✖ 16 = 112

  • Add digit 2 to the result

  • 112 + 9 = 121

  • Hexadecimal 79 is 121 in denary

Examiner Tips and Tricks

Remember that the exam is non-calculator, if you are not confident multiplying and dividing by 16 then use method 1 on both conversions

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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.