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learned something deeper about arithmetic right shift.

so for context, this kind of shift can be used to divide a signed number by some power of two.

if you have an unsigned number, you need only use logical right shift, where zero bits are replaced on the left as you shift right. This works because it's as if each bit stays fixed, but you move the 2^i multipliers. It's as if you multiplied each multiplier by a factor. Then you can factor out the factor, and we see that it's like the entire binary number was multiplied by that factor.

This would be much better with a diagram, but I'm writing this from my phone, so just...try to visualize :)

coming back to the world of unsigned numbers, you have to do the arithmetic right shift. this splats the sign bit on the left as you shift right. why does this work? well, negative numbers are represented in two's complement. to determine their value, you flip the bits and add 1, then ask what number this would be in unsigned, and finally we mentally splat a negative sign there.

the magic is therefore this...the sign bit is two's compliment is actually a zero, due to the flipping. you can think of the +1 as an offset. so when you splat the sign bit, it's as if you are splatting zeros. We already know that this works! that's the magic.