![]() The logic gate level circuit diagram for a full adder is shown above. The highest value a single full adder can add is three. So outputs of 00 equal 0, 01 equal 1, 10 equal 2, and 11 equal 3 in binary. When the sum bit is on it represents a value of 1 and when the carry-out bit is on it has a value of 2. Outputs are binary values that are based on the base 2 number system. Finally when all three inputs are on the carry-out bit and sum bit will be on. If two inputs are on then only the carry-out bit will be on. When only one input is on only the sum bit is on. If all the inputs are off the outputs are off. The truth table shows the value of the output bits carry out and sum based on the input bits A, B, and Carry in. Even though I will show four different ways to build a full adder the truth table is always the same. The truth table for a full adder is shown above. It may be best to use all the same type of logic gate, or it might be best to use the least number of transistors. ![]() The best way to build a full adder will depend on the requirements. I start by showing how to build a half-adder which is more simple but not nearly as useful. In the video above I show the 4 different ways to build a full adder. Black jumper wires are always used to connect to the ground. Different color wires are placed to make each connection type clear. The first three transistors are the first AND gate, the next three transistors are the second AND gate and the final three transistors are the OR gate. On the bottom half of the breadboard are the two AND gates and the OR gate. The first 6 transistors are the first XOR gate and the second 6 transistors are the second XOR gate. On the upper half of the breadboard, the two XOR gates are built. The adder case is therefore 1 + 1 + 0 equals 10. This makes the carry-out on and the sum bit off which makes the output value 10 in binary which is two. The circuit in the photo has inputs A and B on and the carry-in off. While the two LEDs on the right side of the breadboard represent the two output bits. The two LEDs in the upper left corner represent inputs A and B. The inputs are turned on and off by using two dip switches. Inputs A and B come from the positive 5-volt rail on the upper left side of the breadboard. The logic gates used are two XOR gates, two AND gates, and an OR gate. There are a total of 5 logic gates used to build the full adder. The photo above shows a full adder that I built on a breadboard using individual transistors. Full Adder 1 Built With XOR, AND, and OR Logic Gates When two full adders are wired together the output can be 111 which is seven. For example, a single full adder can only add to 11 in binary which is three. This means that a larger number can be summed. ![]() By sending the carry-out bit to the carry-in of the next full adder an extra bit is added to the output. It has two outputs which are the carry-out bit and the sum bit. ![]() A full adder uses multiple logic gates to add inputs A, B, and carry in. ![]()
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