#negative-number

1000 * 60 * 60 * 24 * 30 results in a negative number

You are multiplying ints together, and overflow occurs because the maximum integer is 2^31 - 1. Only after the multiplications does it get converted to a long. Cast the first number as a long. long days_30 = (long) 1000 * 60 * 60 * 24 * 30; or use a long literal: long days_30 = 1000L * 60 * 60 * 24 * 30; That will force long math operations from the start.

Why prefer two’s complement over sign-and-magnitude for signed numbers?

It’s done so that addition doesn’t need to have any special logic for dealing with negative numbers. Check out the article on Wikipedia. Say you have two numbers, 2 and -1. In your “intuitive” way of representing numbers, they would be 0010 and 1001, respectively (I’m sticking to 4 bits for size). In the two’s complement way, they are 0010 and 1111. Now, let’s say I want to add them. Two’s…