iGCSE Computer Science - Distance Learning

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Logical Shifting in Binary (2023 Specification Only)

New 2023 Syllabus Only

In the previous lesson we looked at how Binary addition can be used to by a computer system to make powerful calculations. In this section, we will be looking at performing a logical shift, also known as a Bit Shift can be used to make multiplication & division in binary easier.

binary numbers

Moving binary numbers either left or right along the conversion table is known as a Bit Shift. Moving to the left multiplies by a power of 2, whereas right divides.

Using a logical shift helps make multiplication much quicker than simply adding the numbers together (imagine adding 97 lots of 142!). However, we still need to remember that all a computer can do is count to 2 and load data, save data, and add up… but they do it very very fast!

Whilst it may be possible to multiply binary numbers simply by adding them together, it is more efficient to apply a bit shift as it is a much quicker process. Remember though that this only works if you are attempting to multiply by a power of 2:

Table showing Bit Shift binary multiplication

In the example above, the number 10 is shifted one place to the left to multiply by 2, or two places to the left to multiply by 4. Dividing in this case would require us to shift the same number of places to the right.

In your exam, you will only ever be asked to show a logical shift to multiply or divide by a power of two – anything more complicated won’t be asked in an exam until you reach A Level.