Binary Shifts (AQA GCSE Computer Science)

Revision Note

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Robert Hampton

Written by: Robert Hampton

Reviewed by: James Woodhouse

Binary Shifts

What is a binary shift?

  • A binary shift is how a computer system performs basic multiplication and division

  • 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 left shift of 1?

  • Here is the binary representation of the denary number 40

Binary representation of the decimal number 40 using an 8-bit system, showing bits 0 for 128, 64, 16, 4, 2, 1 and bits 1 for 32, 8.
  • To perform a left binary shift of 1, we move each bit 1 place to the left

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

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

A table showing binary and decimal equivalence. The top row numbers (128 to 1) highlight binary place values. Two rows of binary digits add up to 40 and 80.
  • The original binary representation of denary 40 (32+8)  has multiplied by 2 and became 80 (64+16)

How do you perform a left shift of 2?

  • Here is the binary representation of the denary number 28

A binary table showing bit values for 128, 64, 32, 16, 8, 4, 2, and 1 in blue, with corresponding bits 0, 0, 0, 1, 1, 1, 1, 0 in red below.
  • To perform a left binary shift of 2, we move each bit 2 place to the left

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

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

A binary table shows the values 128 to 1 in blue. Two rows: top with binary "0011100", equating to 28, and bottom with "0111000", equating to 112, highlighted in red.
  • The original binary representation of denary 28 (16+8+4)  has multiplied by 4 and became 112 (64+32+16)

How do you perform a right shift of 1?

  • Here is the binary representation of the denary number 40

A binary number table showing columns labeled 128, 64, 32, 16, 8, 4, 2, and 1. Below them are corresponding values 0, 0, 1, 0, 1, 0, 0, and 0.
  • To perform a right binary shift of 1, we move each bit 1 place to the right

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

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

A table with two binary rows under columns labeled 128 to 1, totaling 40 and 20, showing binary to decimal conversion. The first row reads 00101010, the second 00010100.
  • The original binary representation of denary 40 (32+8)  has divided by 2 and became 20 (16+4)

How do you perform a right shift of 2?

  • Here is the binary representation of the denary number 200

A table showing binary representation of the number 201: top row displays place values (128, 64, 32, 16, 8, 4, 2, 1) and bottom row displays corresponding binary digits (1, 1, 0, 0, 1, 0, 0, 1).
  • To perform a right binary shift of 2, we move each bit 2 places to the right

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

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

A binary to decimal conversion table: two rows of binary numbers, with highlighted values showing 200 in the first row and 50 in the second row.
  • The original binary representation of denary 200 (128+64+8) has divided by 4 and became 50 (32+16+2)

Worked Example

1. Perform a binary shift of 2 places left on the binary number 00001110 [1]

2. Explain the effect of performing a 2 place shift to the left on the binary number 00001110  [2]

Answers

Q1

left-binary-shift
  • Cross out the first 2 digits from the left

  • Write down the binary digits left and add 2 zeros to the end

Q2

  • Multiplies the number by 4

  • Overflow errors can cause loss of precision

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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.