Binary shifts: multiplying and dividing by 2

In denary, adding a 0 on the end multiplies by 10. In binary, moving the bits one place left multiplies by 2. This trick is called a binary shift.

Practise this lesson free (7 questions)

Left shift

A left shift moves every bit one place to the left and puts a 0 in the empty place on the right.
Each left shift multiplies by 2.
00001101 (13) shifted left 1 place = 00011010 (26).
Shifting left 2 places multiplies by 4, and 3 places by 8.

Right shift

A right shift moves every bit one place to the right and puts a 0 in the empty place on the left.
Each right shift divides by 2.
00101000 (40) shifted right 1 place = 00010100 (20).
If a 1 falls off the right end, that part is lost: 00001101 (13) shifted right 1 place = 00000110 (6), not 6.5.

Bits falling off

With 8 bits, a left shift can push a 1 off the left end. Then the answer is wrong, because the number is too big to fit.
StartShiftResultCorrect?
01100100 (100)left 111001000 (200)yes: 100 × 2 = 200
11001000 (200)left 110010000 (144)no: 400 does not fit in 8 bits
Worked example

Shift 00010110 left by 2 places. What happens to its value?

  1. 00010110 = 22.
  2. Move every bit 2 places left and fill with 0s: 01011000.
  3. 01011000 = 88, which is 22 × 4.

Answer: 01011000: the value is multiplied by 4.

Key idea

A left shift of 1 place multiplies by 2; a right shift of 1 place divides by 2. Each extra place doubles the effect. Bits that fall off the end are lost, which can make the answer wrong.

Key words
Binary
A number system that uses only two digits, 0 and 1. Computers store all data in binary.
AND
A Boolean operator that gives True (1) only when both inputs are True.
Denary
The base 10 number system we use every day, with the digits 0 to 9.
Bit
A binary digit: a single 0 or 1. The smallest unit of data.
NOT
A Boolean operator that flips its input: True becomes False and False becomes True.

All KS3 Computing key terms and definitions →

Quick check

Try two quick questions

See if it has sunk in. Answers are marked straight away.

Extra practice

2 more questions

Try each one, then tap to check.

  1. Shift 00000110 left by 1 place. Give the 8-bit answer.

    Show the answer

    Answer: 00001100

    Move every bit 1 place left and fill with 0s: 00001100.

  2. Shift 01100000 right by 2 places. Give the 8-bit answer.

    Show the answer

    Answer: 00011000

    Move every bit 2 places right and fill with 0s: 00011000.

Check you have got it

Answer 7 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.

Practise this lesson free (7 questions)All KS3 Computing lessons

Video for this lesson coming soon. Subscribe on YouTube

Sources and references

Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

Related lessons