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| − | '''Two's complement''' is by far the most common method of representing signed numbers (those that can be either negative or positive) in computing. Any positive integer can be changed into a negative integer by taking its two's complement, and vice versa. Any signed number with a 1 in the highest bit position (the most significant bit, or MSB) is considered to be negative in this system.
| + | #REDIRECT [[sega:Two's complement]] |
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| − | Two's complement is calculated by taking the bitwise NOT of a number (or ''complementing'' it) and adding one to the result. Any carry (overflow) bits are ignored. For instance, to find -7, we would start with the eight-bit binary number 0000 0111:
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| − | !(0000 0111) = 1111 1000
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| − | 1111 1000 + 1 = 1111 1001
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| − | The process is reversable:
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| − | !(1111 1001) = 0000 0110
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| − | 0000 0110 + 1 = 0000 0111
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| − | Let's say we wanted to find the two's complement of 0.
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| − | !(0000 0000) = 1111 1111
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| − | 1111 1111 + 1 = 1 0000 0000 = 0000 0000
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| − | The two's complement of 0 is 0. A negative zero is impossible when using two's complement.
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| − | It is very simple and cheap to implement signed addition when using two's complement, because you do not need to determine the sign beforehand. For example, let's take 5 + -3:
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| − | 0101
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| − | + 1101
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| − | ------
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| − | 10010 = 0010
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| − | The intermediate result is 18, which seems incorrect. But dropping the overflow bit gives us the correct answer of 2. This works for any set of numbers. Note that 5 + (-3) is the same as 5 - 3. It follows that we can use an adder circuit to subtract numbers by taking the two's complement of the subtrahend if the numbers have the same sign.
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| − | [[Category:Hacking Information]]
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