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How does arduino uno cast from long to int?

Does it truncate the bits? (Does it just delete the 16 most left bits?)

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Yes, it just blindly chops off the upper 16 bits. That means that the sign can change between the two.

For instance, 123456789 gets truncated to -13035 and -123456789 truncates to 13035.

To see that in more detail, look at the binary. 123456789 in binary is:

0000 0111 0101 1011 1100 1101 0001 0101

Truncate that at 16 bits and you get:

1100 1101 0001 0101

And of course the high (sign) bit is set, so the value is negative.

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