# Logic and Voltage Behavior of Gates

## 1. Objectives

In this experiment you will investigate the voltage behavior of some physical Integrated Circuit (IC) devices and determine how they can implement logic operations. (For some of you, this material may be review.)

## 2. Materials that you need

### For this lab you will need the following parts:

• protoboard and logic probes and switches
• 1 74'00
• 1 74'02
• 1 74'04
• 1 74'08
• 1 74'32
• 1 74'10

You can find dataseets for these IC circuits on the EE 260L web site.

## 3. Prelab

Follow directions and complete all tasks and questions in the following sections. Write up your solutions into a lab report, and turn it in to your TA in your lab journal. The TA will tell you when to turn in your journal.

Before coming to lab, read this handout and prepare any tables you will need.

### 4.1. Logic Operations

A boolean function is one that operates on bits: its output is a bit, and its inputs are bits. A boolean function can always be expressed as a composition of binary variables and basic logic operations:
• IDENTITY: which doesn't do anything, but is useful in certain situations.
• COMPLEMENT: The complement of the variable X is written as X'.
• AND: The AND of variables X and Y is written as XY.
• OR: The OR of variables X and Y is written as X+Y.
The following are the truth tables for the operations
`     IDENTITY         COMPLEMENT          AND              OR   Input | Output   Input | Output   Input | Output   Input | Output     X   |   X         X  |  X'       X  Y |  XY       X  Y |  X+Y   ------+-------   ------+-------   ------+-------   ------+-------     0   |   0         0  |  1        0  0 |   0       0  0 |   0     1   |   1         1  |  0        0  1 |   0       0  1 |   1                                      1  0 |   0       1  0 |   1                                      1  1 |   1       1  1 |   1`
Figure 4.1. Truth Tables.

Note that the identity operation has only one input, and its output equals the input. The complement operation also has only one input, but the output is opposite of the input. The AND and OR operations have two inputs. For the AND, the output is 1 only if both inputs are 1. The OR output is 1 if at least one of the inputs is 1. Each operation also has a logic symbol which is a graphic of the operation. These symbols are shown in Figure 4.2.

Figure 4.2. Logic Symbols.

The AND operation satisfies the

• Associative Property: A(BC) = (AB)C.
• Commutative Property: AB = BA.
The associative property implies that there is a multi-variable AND operation (rather than just the 2 variable AND operation). Thus, if A, B, C, and D are variables then ABCD is equal to the four variables AND'd together and has the following value
`     ABCD = 1,    if all the variables are "1"          = 0,    if one or more of the variables are "0"`
The commutative property implies that the order of the variables in the AND operation are unimportant (i.e., ABCD = BCAD = DCBA = ...)

The OR operation also satisfies the

• Associative Property: A+(B+C) = (A+B)+C
• Commutative Property: A+B = B+A
The associative property implies that there is a multi-variable OR operation. Thus, if A, B, C, and D are variables then
`    A+B+C+D = 1,    if one or more variables are "1"            = 0,    if all the variables are "0"`
The commutative property implies that the order of the variables in the OR operation are unimportant. Figure 4.3 has the logic symbols for the multi-variable AND and OR operations

Figure 4.3. Multiple variable ANDs and ORs.

These operations are the basic mathematical operators for Boolean algebra. Note that in this subsection we described mathematical things, rather than real, physical things. The operators work with bits (i.e., numbers) which cannot be physically measured.

### 4.2. Some Basic Circuit Components

In this subsection we describe real circuit components, which operate on measurable voltages. The voltages will either be 0 volts or 5 volts, and to indicate 0 volts we write "L" (for Low), and to indicate 5 voltes we write "H" (for High).

The circuit components are the Wire, Voltage Inverter, NAND, NOR, AND, and OR circuits. The Wire can be thought of as a circuit component if we regard one side of the wire as an input and the other side as an output. The voltage table (or function table) of the wire is

`VOLTAGE TABLE FOR WIRE:       Input  |  Output       -------+--------         L    |    L         H    |    H`
A voltage table describes how a combinational circuit's output is a function of its input. In other words, the table describes how the circuit processes the inputs. For the case of a wire, if the input is L then the output is L, and if the input is H then the output is H.

Another device that has a single input and single output is the voltage inverter. Its function table is

`VOLTAGE TABLE FOR INVERTER:       Input  |  Output       -------+--------         L    |    H         H    |    L`
The NAND and NOR circuits have two inputs and one output. Their voltage tables are
`VOLTAGE TABLE FOR NAND:         VOLTAGE TABLE FOR NOR:   Input | Output                  Input | Output   ------+-------                  ------+-------    L  L |  H                       L  L |  H    L  H |  H                       L  H |  L    H  L |  H                       H  L |  L    H  H |  L                       H  H |  L`
The AND and OR circuits also have two inputs and one output. Their voltage tables are
`VOLTAGE TABLE FOR AND:          VOLTAGE TABLE FOR OR:   Input | Output                  Input | Output   ------+-------                  ------+-------    L  L |  L                       L  L |  L    L  H |  L                       L  H |  H    H  L |  L                       H  L |  H    H  H |  H                       H  H |  H`
Note that the AND and OR circuits are different from the AND and OR logic operations. The circuits process voltages, while the logic operations are math operations (functions).

### 4.3. Mixed Logic

We would like the circuits to realize boolean expressions (mathematical functions). In this way, the circuits will act like little "calculators," that process numbers. However, since the circuits process voltages, we need ways to convert voltages (Ls and Hs) to numbers (0s and 1s) and vice versa.

There are two different conventions to convert voltages to bits and vice versa. These are the positive logic convention and the negative logic convention:

`    Positive Logic Convention      Negative Logic Convention        Voltage |  Bit                  Voltage |  Bit        --------+---------              --------+---------           L    |   0                      L    |   1           H    |   1                      H    |   0`
If a circuit is assumed to have the positive logic convention then the L voltage is interpreted as 0, while the H voltage is interpreted as 1. Similarly, if a circuit is assumed to have the negative logic convention then the L voltage is interpreted as 1, while the H voltage is interpreted as 0.

Where does this conversion take place? It's in our head. We have to keep track of the convention being used and appropriately interpret the voltages to bits.

Mixed logic means that parts of the circuit will be positive logic and other parts will be under negative logic. Mixed logic allows us the greatest flexibility in interpreting voltages to bits.

Let's examine how some of the circuits can realize logic operations for us. Consider the NAND circuit. It has the following voltage table

`      Input  | Output      -------+--------       L  L  |   H       L  H  |   H       H  L  |   H       H  H  |   L`
Now assume that the inputs have the positive logic convention. Then in the input columns of the table we can change the Ls to 0s, and the Hs to 1s:
`      Input  | Output      -------+--------       0  0  |   H       0  1  |   H       1  0  |   H       1  1  |   L`
Now assume that the output has the negative logic convention. Then in the output column of the table we can change the Hs to 0s, and L to 1:
`      Input  | Output      -------+--------       0  0  |   0       0  1  |   0       1  0  |   0       1  1  |   1`
Notice that this is the truth table for the AND logic operation. Now let's convert the voltage table of the NAND circuit to a truth table by using negative logic at the inputs, and positive logic at the output:
`      Input  | Output      -------+--------       1  1  |   1       1  0  |   1       0  1  |   1       0  0  |   0`
This is the truth table of the OR logic operation.

The following Figure 3.4 shows two ways to draw a NAND circuit. Note that the "bubbles" in the diagrams indicate the inputs and outputs should be interpreted using negative logic. The inputs and outputs without bubbles are assumed to have positive logic. Hence, the left symbol in the figure implies that the NAND does the AND logical (mathematical) operation if the inputs have positive logic and the output has negative logic. The right symbol in the figure implies that the NAND does the OR logical operation if the inputs have negative logic and the output has positive logic. These drawings are called the mixed logic symbols for the NAND.

Figure 4.4. The mixed logic symbols for the NAND.

Let's consider another circuit, the Wire. Its voltage table is

`       Input | Output       ------+-------         L   |   L         H   |   H`
If we assume positive logic at the input and negative logic at the output, we get the following truth table:
`       Input | Output       ------+-------         0   |   1         1   |   0`
This is the truth table for a complement operation.

If we assume negative logic at the input of the wire and positive logic at the output then the truth table is

`       Input | Output       ------+-------         1   |   0         0   |   1`
Again, this is the truth table for the complement operation. We can conclude that if the input and output of a wire has different logic convention then it does the complement operation. The mixed logic symbols for the wire are shown in Figure 4.5.

Figure 4.5. Mixed logic symbols for the wire.

## 5. Mixed Logic Symbol Exercises

This part of the assignment can be done before lab.
• Task 1: Write down the truth table for the AND circuit assuming positive logic at the inputs and output. Draw the corresponding mixed logic symbol for the circuit.
• Task 2: Write down the truth table for the AND circuit assuming negative logic at the inputs and output. Draw the corresponding mixed logic symbol for the circuit (hence, bubbles should be at the inputs and output).
• Task 3: Write down the truth table for the OR circuit assuming positive logic at the inputs and output. Draw the corresponding mixed logic symbol for the circuit.
• Task 4: Write down the truth table for the OR circuit assuming negative logic at the inputs and output. Draw the corresponding mixed logic symbol for the circuit.
• Task 5: Write down the truth table for the NOR circuit assuming positive logic at the inputs and negative logic at the output. Draw the corresponding mixed logic symbol for the circuit.
• Task 6: Write down the truth table for the NOR circuit assuming negative logic at the inputs and positive logic at the output. Draw the corresponding mixed logic symbol for the circuit.

## 6. Identify the Circuits

You will identify circuits from your parts kits. You will use your protoboard and parts kit to wire different chips and measure voltages. The IC circuits in this experiment have 14 pins as shown in Figure 4.6.

Figure 4.6. 14 pin chip.

### 6.1. 74'04

This chip has six identical circuits, each with a single input and single output as shown in Figure 4.7.

Figure 4.7. A diagram showing the circuits in the 74'04 chip with their pin numbers.

• Task 7: Using the actual 74'04 chip and by measuring voltages, determine the voltage table for one of the circuits. What type of circuit is it (Wire or voltage inverter)?
• Task 8: Suppose the input is negative logic, and the output is positive logic. Using the voltage table, determine the logic operation realized by the circuit. Draw the corresponding mixed logic symbol.
• Task 9: Suppose the input is positive logic, and the output is negative logic. Using the voltage table, determine the logic operation realized by the circuit. Draw the corresponding mixed logic symbol.

### 6.2. 74'00

This chip has four identical circuits, each with two inputs and one output as shown in Figure 4.8.

Figure 4.8. A diagram showing the circuits in the 74'00 chip with their pin numbers.

• Task 10: Using the actual 74'00 chip and by measuring voltages, determine the voltage table for one of the circuits. What type of circuit is it (AND, OR, NAND, or NOR)?

### 6.3. 74'02

This chip has four identical circuits, each with two inputs and one output as shown in Figure 4.9.

Figure 4.9. A diagram showing the circuits in the 74'02 chip with their pin numbers.

• Task 11: Using the actual 74'02 chip and by measuring voltages, determine the voltage table for one of the circuits. What type of circuit is it (AND, OR, NAND, or NOR)?

### 6.4. 74'08

This chip has four identical circuits, each with two inputs and one output as shown in Figure 4.10.

Figure 4.10. A diagram showing the circuits in the 74'08 chip with their pin numbers.

• Task 12: Using the actual 74'08 chip and by measuring voltages, determine the voltage table for one of the circuits. What type of circuit is it (AND, OR, NAND, or NOR)?

### 6.5. 74'32

This chip has four identical circuits, each with two inputs and one output as shown in Figure 4.11.

Figure 4.11. A diagram showing the circuits in the 74'32 chip with their pin numbers.

• Task 13: Using the actual 74'32 chip and by measuring voltages, determine the voltage table for one of the circuits. What type of circuit is it (AND, OR, NAND, or NOR)?

### 6.6. 74'10

This chip has three identical circuits, each with three inputs and one output as shown in Figure 4.12.

Figure 3.12. A diagram showing the circuits in the 74'10 chip with their pin numbers.

• Task 14: Using the actual 74'10 chip and by measuring voltages, determine the voltage table for one of the circuits.
• Task 15: From the voltage table, determine the truth table assuming positive logic at the inputs and negative logic at the output. Draw a corresponding mixed logic symbol for the circuit.
• Task 16: From the voltage table, determine the truth table assuming negative logic at the inputs and positive logic at the output. Draw a corresponding mixed logic symbol for the circuit.

### 6.7. Mystery Circuit

Connect the 74'00 circuit as shown in Figure 4.13. Now we have a circuit with two inputs (I0,I1) and a single output H.

Figure 4.13. This shows how two circuits in the 74'00 chip are connected.

• Task 17: By measuring voltages, determine the voltage table for the circuit.
• Task 18: Determine what the logic convention should be at the inputs and output to make the circuit realize the logical AND operation. Draw the corresponding mixed logic symbol for the circuit.
• Task 19: Determine what the logic convention should be at the inputs and output to make the circuit realize the logical OR operation. Draw the corresponding mixed logic symbol for the circuit.

## 7. What You Turn In

You need to complete the following: