Two's Complement (Cambridge (CIE) IGCSE Computer Science)

Revision Note

Robert Hampton

Written by: Robert Hampton

Reviewed by: James Woodhouse

Two's Complement

What is two's complement?

  • Two's complement is a method of using signed binary values to represent negative numbers

  • Using two's complement the left most bit is designated the most significant bit (MSB)

  • To represent negative numbers this bit must equal 1, turning the column value in to a negative

  • Working with 8 bits, the 128 column becomes -128

-128

64

32

16

8

4

2

1

1

1

1

1

1

1

1

1

= -1

  • In the example above to represent -1, add column values with a 1 to the MSB

    • MSB (-128)

    • Add 64 (-128+64 = -64

    • Add 32 (-64+32 = -32)

    • Add 16 (-32+16 = -16)

    • Add 8 (-16+8 = -8)

    • Add 4 (-8+4 = -4)

    • Add 2 (-4+2 = -2)

    • Add 1 (-2+1 = -1)

  • The two's complement representation of -1 is 11111111

Quick two's complement conversion

  • To represent -76

  • Write out the positive version of the number

128

64

32

16

8

4

2

1

0

1

0

0

1

1

0

0

= 76

  • Starting from the least significant bit (right most column), copy out the binary values up to and including the first 1

-128

64

32

16

8

4

2

1

1

0

0

  • For the remaining digits, invert them (0s to 1s/1s to 0s)

-128

64

32

16

8

4

2

1

1

0

1

1

0

1

0

0

  • -128 + 32 + 16 + 4 = -76

  • The two's complement representation of -76 is 10110100

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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.