In this chapter, we define binary adders. An adder is a combinational circuit that implements the function f (x, y) = x + y. To be more precise, we want the function f to be a Boolean function, not a function defined over the integers. We therefore use binary representation. This means that the inputs are two n-bit strings, where each string represents a nonnegative integer in binary representation. The output should represent their sum in binary representation.
One complication that we must address if we wish to be precise is that the sum might be too large and cannot be represented using n bits. We solve this problem by adding one bit to the output, called the carry-out bit.
We present three different combinational ...