You can find dataseets for these IC circuits on the EE 260L web site.
Before coming to lab, read this handout and prepare any tables you will
need.
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
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
ABCD = 1, if all the variables are "1"The commutative property implies that the order of the variables in the AND operation are unimportant (i.e., ABCD = BCAD = DCBA = ...)
= 0, if one or more of the variables are "0"
The OR operation also satisfies the
A+B+C+D = 1, if one or more variables are "1"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
= 0, if all the variables are "0"
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.
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: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.
Input | Output
-------+--------
L | L
H | H
Another device that has a single input and single output is the voltage inverter. Its function table is
VOLTAGE TABLE FOR INVERTER:The NAND and NOR circuits have two inputs and one output. Their voltage tables are
Input | Output
-------+--------
L | H
H | L
VOLTAGE TABLE FOR NAND: VOLTAGE TABLE FOR NOR:The AND and OR circuits also have two inputs and one output. Their voltage tables are
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
VOLTAGE TABLE FOR AND: VOLTAGE TABLE FOR OR: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).
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
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 ConventionIf 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.
Voltage | Bit Voltage | Bit
--------+--------- --------+---------
L | 0 L | 1
H | 1 H | 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 | OutputNow 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:
-------+--------
L L | H
L H | H
H L | H
H H | L
Input | OutputNow 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:
-------+--------
0 0 | H
0 1 | H
1 0 | H
1 1 | L
Input | OutputNotice 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:
-------+--------
0 0 | 0
0 1 | 0
1 0 | 0
1 1 | 1
Input | OutputThis is the truth table of the OR logic operation.
-------+--------
1 1 | 1
1 0 | 1
0 1 | 1
0 0 | 0
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 | OutputIf we assume positive logic at the input and negative logic at the output, we get the following truth table:
------+-------
L | L
H | H
Input | OutputThis is the truth table for a complement operation.
------+-------
0 | 1
1 | 0
If we assume negative logic at the input of the wire and positive logic at the output then the truth table is
Input | OutputAgain, 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.
------+-------
1 | 0
0 | 1
Figure 4.5. Mixed logic symbols for the wire.
Figure 4.6. 14 pin chip.
Figure 4.7. A diagram showing the circuits in the 74'04 chip with
their pin numbers.
Figure 4.8. A diagram showing the circuits in the 74'00 chip with
their pin numbers.
Figure 4.9. A diagram showing the circuits in the 74'02 chip with
their pin numbers.
Figure 4.10. A diagram showing the circuits in the 74'08 chip with
their pin numbers.
Figure 4.11. A diagram showing the circuits in the 74'32 chip with
their pin numbers.
Figure 3.12. A diagram showing the circuits in the 74'10 chip with
their pin numbers.
Figure 4.13. This shows how two circuits in the 74'00 chip are connected.