MultiMedia Logic is a free application for learning how to design Boolean circuits, such as multiplexers, half adders and full adders. Logical adders perform binary addition on two arbitrarily large base-two numbers. The difference between a full adder and a half adder is that a full adder handles a carry-over bit while a half adder omits this number. Therefore, a full adder requires three input bits and two output bits, while a half adder only uses two inputs and one output.
Go to a website that displays a full adder diagram (link in Resources); if you're a student, refer to the diagram in your textbook. A basic full adder isn't very complicated, but a diagram illustrates the exact wiring of inputs, gates and outputs.
Open MultiMedia Logic, select the “Input” tool from the toolbox, and then add three inputs to the canvas by clicking where you want to place them. Name the inputs “A,” “B” and “Cin” by clicking an input's name and typing the new name.
Select the “LED” tool, and then create two LED outputs. In a real logic gate, the outputs are wired to another logic gate or hardware component, but in MultiMedia Logic, an LED light represents the output's Boolean value. Name the LEDs “S” and “Cout.”
Select the “Xor” tool, and then add two Xor gates between the inputs and outputs. An Xor gate performs an exclusive-or operation on two input bits, outputting “true” if exactly one input is true or “false” in every other case.
Select the “And” tool, and then add two And gates between the inputs and outputs. Select the “Or” tool, and then add one Or gate. In total, a basic full adder uses five gates: two Xor gates, two And gates and one Or gate.
Select the “Wire” tool, and then connect the inputs to the gates according to the wiring diagram. To connect two objects using the Wire tool, click the first object, and then hold the mouse button and drag the cursor to the second object. To connect an input to more than one gate, click the wire connecting the input to its initial gate, and then hold the mouse button and drag the cursor to the next gate.
Connect A and B to the inputs of an Xor gate, and then connect them to the inputs of an And gate as well.
Connect Cin and the output of the first Xor gate to the inputs of the second Xor gate, and then connect both of those wires to the inputs of the unused And gate as well.
Connect the outputs of both And gates to the inputs of the Or gate.
Connect the output of the second Xor gate to S and connect the output of the Or gate to Cout. The full adder's wiring is complete.
Click “Play” in the toolbar to explore the full adder's function. Click an input to switch it on and send a “true” signal from its output. Refer to the truth table on the College of the Redwoods site (see Resources) or your textbook for a full adder's correct output. When the S LED lights up, it represents a “true” value or “one” in the sum row; when the Cout LED lights up, it represents a carry-over value to add to the next column in the operation.