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Logical Binary Shifts

In the previous section 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 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.

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:

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.

So what if we needed to multiply by a number that isn’t a power of 2? This can be achieved by combining a bit shift and binary addition.

In the example below, we are multiplying 10 by 3. To do this:

  1. shift to multiply by 2.
  2. add another 10 ( *1)
  3. add the shift and extra 10 together
Binary Bit Shift Plus Addition For Multiplication

Activity – Notes

The Binary Multiplication / Bit Shifting Notes provide a structured way for students to revise topic areas covered in class in a visual way. Encourage students to colour in areas of importance, add doodles and colour, then add more detail to the notes page being as creative as possible.