Signed to unsigned with subtraction

Question

I've recently decided to make the leap and read through a bunch of computer science books to better equip myself for the future.

At the moment I'm reading through converting signed to unsigned decimals. I understand the majority if it (hopefully it becomes easier to eventually), but struggling with the following (in 32-bit):

-2147483647-1U < -2147483647

According the book, this evaluates to true. There's a bit about this that I'm still struggling with as I cant see why it evaluates to this.

With my understanding, I know that they are both converted to unsigned values in this calculation due to the first number being cast as unsigned. The first number is therefore -2147483648 after subtraction and then converted to unsigned, or does that unsigned conversion happen prior to the subtraction?

Sorry for the lengthy post, just trying to get my head around understanding this.

Thanks!

Answer 1

The first number is therefore -2147483648 after subtraction

Not quite. With -2147483647-1U, the conversion to unsigned happens first. With mixed int/unsigned math, the int is converted to an unsigned.

Subtracting unsigned form an int results in an unsigned and an unsigned is never negative.

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-2147483647-1U < -2147483647

Assume 32-bit or wider unsigned/int

-2147483647-1U is a int minus an unsigned, so -2147483647 is converted to unsigned 2147483649 and the difference is unsigned 2147483648. Now an unsigned is compare to an int, so the int is converted to unsigned 2147483649. The left is less than the right, so the result is true.

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[Edit]

Assume narrower than 32-bit unsigned/int, yet long uses the common 2's complement encoding. Often seen in embedded 8/16-bit processors in 2017.

-2147483647-1U is a long minus a narrower unsigned, so -2147483647 remains a long and 1U is converted to int 1 and the difference is long -2147483648. Now an long is compare to an long. The left is less than the right, so the result is true.