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The sum output (S) can be produced from the inputs by connecting two 2-input XOR gates as shown in Figure 4. We will use only 2-input gates in the implementation portion of this lab, so your design can only use 2-input gates.
Rom the truth table, we now want to implement our design using logic gates.
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Table 1: Partially completed truth table for full adder The values for S (sum) are given, but the Cout (carry out) column is left blank.Ĭomplete the table by filling in the correct values for Cout so that adders connected as in Figure 2 will perform valid addition. As is common, the inputs are shown in binary numeric order. The table indicates the values of the outputs for every possible input, and thus completely specifies the operation of a full adder. To save you design time, however, you will only build a full adder in this lab.Ī partially completed truth table for a full adder is given in Table 1. A half adder is similar to a full adder, except that it lacks a Cin and is thus simpler to implement. This would allow us to use a half adder for the first bit of the sum. Note that the rightmost Cin input is unnecessary, since there can never be a carry into the first column of the sum. Each bit of the 3-bit numbers being added is connected to the appropriate adder’s inputs and the three sum outputs (S2:0) make up the full 3-bit sum result. The Cout for each bit is connected to the Cin of the next most significant bit.
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Figure 2 shows how to build a circuit that adds two 3-digit binary numbers using three full adders. When a sum is performed using full adders, each adder handles a single column of the sum. Finally, you add the most significant bits (with no carry) and get a 1 in the most significant bit of the sum. Then you add the next two bits with the carry, and place a 1 in the second bit of the sum. Since 1+1=10 (in binary), you place a zero in the least significant bit of the sum and carry the 1. To understand how these signals are used, consider how you would add the binary numbers 101 and 001 by hand:Īs with decimal addition, you first add the two least significant bits. The Cin (carry in) and Cout (carry out) signals are used when adding numbers that are more than one bit long. Inputs A and B each represent 1-bit binary numbers that are being added, and S represents a bit of the resulting sum. The full adder will be an integral part of the microprocessor that you design in later labs.Ī full adder has three inputs (A, B, Cin) and two outputs (S, Cout), as shown in Figure 1. Since adders are needed to perform arithmetic, they are an essential part of any computer. If you would like to work from the convenience of your own computer, see the class website for instructions on installing the tools.Īn adder, not surprisingly, is a circuit whose output is the binary sum of its inputs. The computer-aided design (CAD) tools required for this class are installed in the lab (Edgerly 207). Refer to the “What to Turn In” section at the end of this handout before beginning the lab. You will also build your adder on a breadboard using discrete chips to get a more tactile sense of digital logic.Īfter completing the lab, you are required to turn in something from each part.
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Along the way, you will learn to use the Altera field-programmable gate array (FPGA) tools to enter a schematic, simulate your design, and download your design onto a chip. In this lab you will design a simple digital circuit called a full adder.