W4 Digital Electronics Assignment and Lab

Boolean operators, like mathematical operators, have a standard precedence, or order of operation. The invert operator has the highest precedence and the AND operator takes precedence over the OR operator, but parentheses alter the precedence of these operators. The expressions for the NAND and NOR gates, for example, require parentheses so that the entire expression, rather than just one variable, is inverted.

You can use Boolean algebra to simplify logic expressions, as well as represent and evaluate logic functions.Boolean algebra has 12 basic rules that summarize functionally equivalent logic expressions. These rules allow you to work through and simplify more complex Boolean expressions. In Part 1 of this experiment, you will use Multisim to verify these rules.

Two additional theorems for working with Boolean expressions are DeMorgan’s theorems. These theorems mathematically verify that NAND gates are equivalent to negative-OR gates, and that NOR gates are equivalent to negative-AND gates. The theorems are useful for simplifying expressions with inverted inputs and outputs and working with negative logic, in which 0 rather than 1 is the active logic level. In Part 2 of this experiment, you will use Multisim to verify DeMorgan’s theorems.

Reading

Kleitz, Digital Electronics: A Practical Approach with VHDL, 9th Edition, Chapter 5.

Multisim Files

Part 1: Digital_Exp_04_Part_01a through Digital_Exp_04_Part_01q.

Part 2: Digital_Exp_04_Part_02a and Digital_Exp_04_Part_02b.

Key Objectives

Part 1: Verify the validity of the 12 rules of Boolean algebra.

Part 2: Verify the validity of DeMorgan’s theorems.

Part 1: Boolean Algebra

4.0 Laws of Boolean Algebra

For each of the Multisim files listed in Table 4-1:

1) Open the file.

2) Verify that the logic driving each probe corresponds to the indicated logic expression.

3) Run the simulation.

4) Set the circuit switches to each setting listed in the circuit file.

5) Specify in the table whether the states for each probe in the circuit are identical for all switch positions.

6) Stop the simulation.

4.1 Rules of Boolean Algebra

For each of the Multisim files listed in Table 4-2:

1) Open the file.

2) Verify that the logic driving each probe corresponds to the indicated logic expression.

3) Run the simulation.

4) Set the circuit switches to each setting listed in the circuit file.

5) Specify in the table whether the states for each probe in the circuit are identical for all switch positions.

6) Stop the simulation.

Questions for Part 1

1) What principle was used to verify the laws and rules of Boolean algebra?

2) Using the rules of Boolean algebra, what is the simplified expression for AA + AB + AC?

3) From Rules 3 and 4, how can a 2-input AND gate be used to selectively pass or block a signal?

Part 2: DeMorgan’s Theorems

4.2 NAND Gate Equivalent

1) Open the Multisim file Digital_Exp_04_Part_02a .

2) Run the simulation.

3) Apply the switch inputs shown in Table 4-3. Record the states (unlit = 0, lit = 1) of the probe for (AB)’ and the probe for A’ + B’ for each switch setting.

Table 4-3: Results of Nand Equivalent Switch Settings

4) Stop the simulation and summarize your observations.

4.3 NOR EQUIVALENT

1) Open the Multisim file Digital_Exp_04_Part_02b .

2) Run the simulation.

3) Apply the switch inputs shown in Table 4-4. Record the states (unlit = 0, lit = 1) of the probe for (A + B)’ and the probe for A’ B’ for each switch setting.

Table 4-4: Results of Nor Equivalent Switch Settings

4) Stop the simulation and summarize your observations.

Questions for Part 2

1) Using DeMorgan’s Theorems, what is an equivalent expression for ((A + B)’(C + D)’)’?

2) You wish to implement a circuit that will output X = 1 if either input A or B is 0. What gate should you use?