6.5: Conclusion

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The adder forms the basis for all of the arithmetic functions in the ALU. Subtraction, multiplication, and division all are implemented using algorithms which are based on the adder. The adder is therefore a stand in for all of the other types of functions performed by the ALU.

Despite the appearance that addition is more complex, it can be implemented as a Boolean function consisting only of AND, OR, and XOR gates. These simple Boolean functions are implemented in circuits called half adders and full adders. It is when these functions are chained together so that the carry from each previous function is used in the next function that the adder can add larger numbers.

The implementation of the full adder circuit is more complex than the other circuits which have been looked at so far. It required 3 different chips, 2 outputs, and 5 gates that had to be connected. This circuit required some degree of carefulness and forethought to implement and debug it.

The adder was the first circuit implemented in this text that is a component, and it has been encapsulated as an IC. The 7482 (2-bit binary full adder) and 7483 (4-bit binary full adder) IC chips are implementations of this circuit.