- Lesson 5 Lab

Topics: All-NAND decoder; 2-bit adder

Submission: report uploaded to RioLearn

LogicWorks files to create: All tasks: two types of logic circuits (gates and chip schematic)

Required ICs: (2) NAND 7400, (1) XOR 7486, (1) AND 7408, (1) OR 7432

Task 1: Custom decoder entirely from NAND gates

Remember the custom decoder from the previous lab (output is ON for input of decimal 0, 2, 8, 10, 12, or 13)? Build a circuit that accomplishes the same thing, but build it using only NAND chips (hint: if you simplify, you should be able to do this with 8 gates).

In report:

Describe the problem and define universal gate

Illustrate procedure to convert from AND-OR logic circuit to all-NAND logic circuit

Images of all-NAND logic circuit, chip schematic (remember only 2-input gates)

Algebraic proof that the two circuits produce the same logic

Discuss the pros and cons of using only NAND gates (possible topics: cost, propagation delays, final logic, design time, ability to understand the circuit)

Task 2: 2-bit adder

Design and build a circuit that can add together two 2-bit numbers (with a carry-in). Figure 1 illustrates this in two ways: symbolically and with a specific numeric example.

Figure 1: 2-bit addition with a carry-in. Left side shows this symbolically. Right side provides a specific numeric example.

Figure 2 provides the logic circuit for a full adder (or a 1-bit adder). Use this schematic as the basis for your design. In order to make a 2-bit adder, you will need two full adders that are connected in a special way. In LogicWorks, build your design first as logic gates (to verify that it works), then with chip schematics (for ease of wiring).

Figure 2: Logic circuit for a full adder

In report:

Describe the objective. In the process, explain how binary addition works.

Describe and illustrate your design process. Place a special emphasis on the connection between longhand addition and how your 2-bit adder is constructed.

The formal design process would have included a truth table. How many rows would be needed in that truth table? Discuss the pros and cons of the formal design process and the process used here.