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Adding Binary Numbers A key requirement of digital computers is the ability to use logical functions to perform arithmetic operations. The basis of this is addition; if we can add two binary numbers, we can just as easily subtract them, or get a little fancier and perform multiplication and division. How, then, do we add two binary numbers? Let's start by adding two binary bits. Since each bit has only two possible values, 0 or 1, there are only four possible combinations of inputs. These four possibilities, and the resulting sums, are: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 Whoops! That fourth line indicates that we have to account for two output bits when we add two input bits: the sum and a possible carry. Let's set this up as a truth table with two inputs and two outputs, and see where we can go from there. INPUTS OUTPUTS Well, this looks familiar, doesn't it? The Carry output is a simple AND function, and the Sum is an Exclusive-OR. Thus, we can use two gates to add these two bits together. The resulting circuit is shown below. A

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