dsp puzzle - Gaussian FIR filter with no multipliers?

What is the simplest way to implement a Gaussian FIR filter with unity gain coefficients and no multipliers?

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Note: A Gaussian FIR filter is an FIR filter with an impulse response that is a Gaussian function. By "unity-gain coefficients" I mean all coefficients in the filter structure are 1.

Answer

This is an approximation, but you can make it as good as you like.

Just use a cascade of several filters with rectangular impulse responses. In the simplest case this would be a two-tap filter. This works because of the central limit theorem. However, you will need to scale, because otherwise your resulting impulse response may become too large. The scaling could be done by bit-shifting.