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Asked: 2026-05-25T10:40:08+00:00

Using only adding, subtracting, and bitshifting, how can I multiply an integer by a

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Using only adding, subtracting, and bitshifting, how can I multiply an integer by a given number?

For example, I want to multiply an integer by 17.

I know that shifting left is multiplying by a multiple of 2 and shifting right is dividing by a power of 2 but I don’t know how to generalize that.

What about negative numbers? Convert to two’s complement and do the same procedure?

(EDIT: OK, I got this, nevermind. You convert to two’s complement and then do you shifting according to the number from left to right instead of right to left.)

Now the tricky part comes in. We can only use 3 operators.

For example, multiplying by 60 I can accomplish by using this:

(x << 5) + (x << 4) + (x << 3) + (x << 2)

Where x is the number I am multiplying. But that is 7 operators – how can I condense this to use only 3?

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1 Answer

  1. Editorial Team

    As far as I know, there is no easy way to multiply in general using just 3 operators.

    Multiplying with 60 is possible, since 60 = 64 – 4: (x << 6) - (x << 2)

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