Binary Shifts (Cambridge (CIE) IGCSE Computer Science)

Revision Note

Robert Hampton

Written by: Robert Hampton

Reviewed by: James Woodhouse

Binary Shifts

What is a logical binary shift?

  • A logical binary shift is how a computer system performs basic multiplication and division on non-negative values (0 and positive numbers)

  • Binary digits are moved left or right a set number of times

  • A left shift multiplies a binary number by 2 (x2)

  • A right shift divides a binary number by 2 (/2)

  • A shift can move more than one place at a time, the principle remains the same

  • A left shift of 2 places would multiply the original binary number by 4 (x4)

How do you perform a logical left shift of 1?

  • Here is the binary representation of the denary number 40

128

64

32

16

8

4

2

1

0

0

1

0

1

0

0

0

  • To perform a left logical binary shift of 1, we move each bit 1 place to the left

  • The digit in the 128 column (MSB) will move left causing an overflow error

  • The 1 column becomes empty so is filled with a 0

128

64

32

16

8

4

2

1

 

0

1

0

1

0

0

0

= 40

0

1

0

1

0

0

0

0

= 80

  • The original binary representation of denary 40 (32+8)  was multiplied by 2 and became 80 (64+16)

How do you perform a logical left shift of 2?

  • Here is the binary representation of the denary number 28

128

64

32

16

8

4

2

1

0

0

0

1

1

1

0

0

  • To perform a left binary shift of 2, we move each bit 2 places to the left

  • The digit in the 128 (MSB) and 64 column will move left causing an overflow error

  • The 1 and 2 column become empty so are filled with a 0

128

64

32

16

8

4

2

1

 

0

1

1

1

0

0

= 28

0

1

1

1

0

0

0

0

= 112

  • The original binary representation of denary 28 (16+8+4)  was multiplied by 4 and became 112 (64+32+16)

How do you perform a logical right shift of 1?

  • Here is the binary representation of the denary number 40

128

64

32

16

8

4

2

1

0

0

1

0

1

0

0

0

  • To perform a right binary shift of 1, we move each bit 1 place to the right

  • The digit in the 1 column (LSB) will  move right causing an underflow error

  • The 128 column becomes empty so is filled with a 0

128

64

32

16

8

4

2

1

 

0

0

1

0

1

0

0

= 40

0

0

0

1

0

1

0

0

= 20

  • The original binary representation of denary 40 (32+8)  was divided by 2 and became 20 (16+4)

How do you perform a logical right shift of 2?

  • Here is the binary representation of the denary number 200

128

64

32

16

8

4

2

1

1

1

0

0

1

0

0

0

  • To perform a right binary shift of 2, we move each bit 2 places to the right

  • The digits in the 1 (LSB) and 2 columns will move right causing an underflow error

  • The 128 and 64 columns become empty so are filled with a 0

128

64

32

16

8

4

2

1

 

1

1

0

0

1

0

= 200

0

0

1

1

0

0

1

0

= 50

  • The original binary representation of denary 200 (128+64+8) was divided by 4 and became 50 (32+16+2)

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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.