Skip to content
VirtusAcademy

Binary Shifts

FoundationHigherAQA

Practise Binary Shifts for GCSE Computer Science with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers. A left shift multiplies a binary number by two, and a right shift divides it by two.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA specification. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A binary shift moves every bit left or right by a given number of places, and it has a precise arithmetic effect.

Shifting left by one place multiplies the value by 2. Shifting left by n places multiplies by 2 to the power n. Zeros are added on the right to fill the gap, and bits shifted off the left end are lost.

Shifting right by one place divides by 2. Zeros are added on the left, and bits shifted off the right are lost — which means precision is lost if the number was odd. Shifting 1011, which is 11, right by one gives 0101, which is 5 rather than 5.5. This loss is a required exam point, not an incidental detail.

Revision notes

Shifting left

Each place shifted left multiplies the value by 2.

Shifting left by n places multiplies by 2ⁿ. Zeros fill the gap on the right. Bits shifted off the left end are lost, which can cause overflow.

Shifting right

Each place shifted right divides the value by 2.

Zeros fill the gap on the left. Bits shifted off the right end are lost, so any remainder is discarded and precision is lost.

The precision point

Shifting 1011 (11 in denary) right by one gives 0101, which is 5 rather than 5.5.

The rightmost 1 has been shifted off the end and lost. Stating this loss of precision is required for full marks whenever a right shift is examined.

Key points

  • A left shift multiplies by 2 each place.
  • A left shift of n places multiplies by 2ⁿ.
  • Zeros fill the gap left behind.
  • A right shift divides by 2 each place.
  • Bits shifted off the end are lost.
  • A right shift can lose precision.

Worked examples

Example 1

Shift the binary number 0011 left by two places and state the denary result. [3 marks]

Working

0011 is 3 in denaryconvert the starting value
Shifting left two places gives 1100, with zeros filling the rightperform the shift
1100 is 12, which is 3 × 2² = 12state the denary result

Example 2

Shift 1011 right by one place and explain what is lost. [3 marks]

Working

1011 is 11 in denaryconvert the starting value
Shifting right one place gives 0101, which is 5perform the shift
The rightmost 1 is shifted off the end and lost, so 5.5 becomes 5 and precision is lostexplain the loss

Example 3

State the effect on the denary value of shifting a binary number left by three places. [2 marks]

Working

Each place shifted left multiplies the value by 2state the effect per place
so three places multiplies by 2³ = 8work out the overall effect

Common mistakes

  • Saying a right shift always divides exactly.

    Precision is lost when a 1 is shifted off the end.

  • Filling the gap with 1s.

    Zeros are added.

  • Confusing the direction with the operation.

    Left multiplies, right divides.

  • Forgetting to mention lost bits.

    Bits shifted off the end are lost, which is examinable.

Exam tips

  • Convert to denary to check your shift.
  • State the multiplication or division factor.
  • Mention lost precision on right shifts.
  • Fill gaps with zeros.

Key terms

Binary shift
Moving all bits left or right by a number of places.
Left shift
A shift multiplying the value by a power of 2.
Right shift
A shift dividing the value by a power of 2.
Precision loss
Information lost when bits are shifted off the end.

Related topics

Written and reviewed against the current AQA specification. Spotted an error? Let us know.