Chapter 4 Exercises and Answers

Chapter 4 Exercises and Answers Answers are in blue, except for circuit diagrams. For Exercises 1- 17, mark the answers true and false as follows:
A. True
B. False |1. |Logic diagrams and truth tables are equally powerful in |
| |expressing the processing of gates and circuits. |
| |A |
|2. |Boolean expressions are more powerful than logic diagrams in |
| |expressing the processing of gates and circuits. |
| |B |
|3. |A NOT gate accepts two inputs. |
| |B |
|4. |The output value of an AND gate when both inputs are 1 is 1. |
| |A |
|5. |The AND and OR gates produce opposite results for the same |
| |input |
| |B |
|6. |The output value of an OR gate when both inputs are 1 is 1. |
| |A |
|7. |The output of an OR gate when one input is 0 and one input is 1|
| |is 0. |
| |B |
|8. |The output value of an XOR gate is 0 unless both inputs are 1. |
| |B |
|9. |The NOR gate produces the opposite results of the XOR gate. |
| |B |
|10. |A gate can be designed to accept more than two inputs. |
| |A |
|11. |A transistor is made of semiconductor material. |
| |A |
|12. |Inverting the output of an AND gate is equivalent to inverting |
| |the individual signals first, then passing them through an OR |
| |gate. |
| |A (Demorgan's law) |
|13. |The sum of two binary digits (ignoring the carry) is expressed |
| |by an AND gate. |
| |B |
|14. |A full adder takes the carry-in value into account. |
| |A |
|15. |A multiplexer adds all of the bits on its input lines to |
| |produce its output. |
| |B |
|16. |Integrated circuits are classified by the number of gates |
| |contained in them. |
| |A |
|17. |A CPU is an integrated circuit. |
| |A |
For Exercises 18 - 29, match the gate with the diagram or description of
the operation.
A. AND
B. NAND
C. XOR
D. OR
E. NOR
F. NOT |18. |Inverts its input. |
| |F |
|19. |Produces a 1 only if all its inputs are 1 and a 0 otherwise. |
| |A |
|20. |Produces a 0 only if all its inputs are 0 and a 1 otherwise. |
| |D |
|21. |Produces a 0 only of its inputs are the same and a 1 otherwise.|
| | |
| |C |
|22. |Produces a 0 of all its inputs are all 1 and a 1 otherwise. |
| |B |
|23. |Produces a 1 if all its inputs are 0 and a 0 otherwise. |
| |E |
|24. |[pic] |
| |F |
|25. |[pic] |
| |A |
|26. |[pic] |
| |D |
|27. |[pic] |
| |C |
|28. |[pic] |
| |B |
|29. |[pic] |
| |E |
Exercises 30 - 73 are short answer or design questions.
|30. |How is voltage level used to distinguish between binary digits?|
| | |
| |A voltage level in the range of 0 to 2 volts is interpreted as |
| |a binary 0. A voltage level in the range of 2+ to 5 volts is |
| |interpreted as a binary 1. |
|31. |Distinguish between a gate and a circuit. |
| |A gate accepts one or more input signals and produces an output|
| |signal. Each type of gate performs one logical function. A |
| |circuit is a combination of gates designed to accomplish a more|
| |complex logical function. |
|32. |What are the three notational methods for describing the |
| |behavior of gates and circuits? |
| |Boolean expressions, logic diagrams, and truth tables |
|33. |Characterize the notations asked for in Exercise 32. |
| |Boolean expressions use the operations of Boolean algebra to |
| |describe the behavior of gates and circuits. Logic diagrams use|
| |a graphical representation to describe the behavior of gates |
| |and circuits. Truth tables define the behavior of gates and |
| |circuits by showing all possible input and output combinations |
| |of the gates and circuits. |
|34. |How many input signals can a gate receive and output signals |
| |can a gate produce? |
| |A gate can accept one or more input signals, but can produce |
| |only a single output value. |
|35. |Name six types of gates. |
| |NOT, AND, OR, XOR, NAN, NOR |
|36. |Give the three representations of a NOT gate and say in words |
| |what NOT means. |
A is the input signal and X is the output signal.
Boolean expression: X = A'
Logic Diagram:
[pic]
Truth Table:
A X
0 1
1 0
NOT takes a binary input value and inverts it. |37. |Give the three representations of an AND gate and say in words |
| |what AND means. |
A and B are the input signals and X is the output signal.
Boolean expression: A ( B (A AND B)
Logic Diagram:
|[pic] |
Truth Table:
A B X
0 0 0
0 1 0
1 0 0
1 1 1
If both input values are 1, AND returns a 1; otherwise AND returns a 0.
|38. |Give the three representations of an OR gate and say in words |
| |what OR means. |
A and B are the input signals and X is the output signal.
Boolean expression: A + B (A OR B)
Logic Diagram:
|[pic] |
Truth Table
A B X
0 0 0
0 1 1
1 0 1
1 1 1
If both input values are 0, OR returns 0; otherwise OR returns a 1.
|39. |Give the three representations of an XOR gate and say in words |
| |what XOR means. |
A and B are the input signals and X is the output signal.
Boolean expression: A ( B (A XOR B)
Logic Diagram:
|[pic] |
Truth Table
A B X
0 0 0
0 1 1
1 0 1
1 1 0
If both inputs are the same value, XOR returns a 0; otherwise XOR
returns a 1.
|40. |Give the three representations of a NAND gate and say in words |
| |what NAND means. |
A and B are the input signals and X is the output signal.
Boolean expression: (A ( B)' (NOT (A AND B))
Logic Diagram:
|[pic] |
Truth Table
A B X
0 0 1
0 1 1
1 0 1
1 1 0
If the inputs are different or both 0, NAND returns a 1; if both are 1,
it returns a 0.
|41. |Give the three representations of a NOR gate and say in words |
| |what NOR means. |
A and B are the input signals and X is the output signal.
Boolean expression: (A + B)' (NOT (A AND B))
Logic Diagram:
|[pic] |
Truth Table
A B X
0 0 1
0 1 1
1 0 1
1 1 0
If the inputs are both 0, NOR returns a 1; otherwise NOR returns a 0.
|42. |Compare and contrast the AND gate and the NOR gate. |
| |An AND gate produces a 1 as output only if both in