Questions and Answers of Essentials Of Computer Organization

Perform the following binary divisions, assuming unsigned integers:a) 101101 ÷ 101b) 10000001 ÷ 101c) 1001010010 ÷ 1011
Perform the following binary divisions, assuming unsigned integers:a) 11111101 ÷ 1011b) 110010101 ÷ 1001c) 1001111100 ÷ 1100
Use the double-dabble method to convert 10212 directly to decimal. (Hint: You have to change the multiplier.)
Using arithmetic shifting, perform the following:a) Double the value 00010101 .b) Quadruple the value 01110111 .c) Divide the value 11001010 in half.
Using the model in the previous question, including your chosen bias, add the following floating-point numbers and express your answer using the same notation as the addend and augend:Calculate the
Let a = 1.0 × 2 , b = −1.0 × 2 and c = 1.0 × 2 . Using the simple floating-point model described in the text (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15,
Show how each of the following floating-point values would be stored using IEEE-754 single precision (be sure to indicate the sign bit, the exponent, and the significand fields):a) 12.5b) −1.5c)
Show how each of the following floating-point values would be stored using IEEE-754 double precision (be sure to indicate the sign bit, the exponent, and the significand fields):a) 12.5b) −1.5c)
a) The ASCII code for the letter A is 1000001, and the ASCII code for the letter a is 1100001. Given that the ASCII code for the letter G is 1000111, without looking at Table 2.7, what is the ASCII
Decode the following ASCII message, assuming 7-bit ASCII characters and no parity:1001010 1001111 1001000 1001110 0100000 1000100 1001111 1000101
Why would a system designer wish to make Unicode the default character set for their new system? What reason(s) could you give for not using Unicode as a default? (Hint: Think about language
Suppose we are given the following subset of code words, created for a 7-bit memory word with one parity bit: 11100110, 00001000, 10101011, and 11111110. Does this code use even or odd parity?
Compute the Hamming distance of the following code:0011010010111100 0000011110001111 0010010110101101 0001011010011110
Compute the Hamming distance of the following code:0000000101111111 0000001010111111 0000010011011111 0000100011101111 0001000011110111 0010000011111011 0100000011111101 1000000011111110
Suppose we want an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 10.a) How many parity bits are necessary?b) Assuming we are using the Hamming
Repeat exercise 68 using the following code word:0 1 1 1 1 0 1 0 1 0 1
Name two ways in which Reed-Solomon coding differs from Hamming coding.
3. Which Boolean operation is referred to as a Boolean sum?
5. What is the Boolean duality principle?
7. What is the relationship between transistors and gates?
8. What is the difference between a gate and a circuit?
9. Name the four basic logic gates.
10. What are the two universal gates described in this chapter? Why are these universal gates important?
11. Describe the basic construction of a digital logic chip.
12. Describe the operation of a ripple-carry adder. Why are ripple-carry adders not used in most computers today?
13. What are the three methods we can use to express the logical behavior of Boolean functions?
14. What are the necessary steps one must take when designing a logic circuit from a description of the problem?
15. What is the difference between a half-adder and a full adder?
17. What kind of circuit selects binary information from one of many input lines and directs it to a single output line?
18. How are sequential circuits different from combinational circuits?
19. What is the basic element of a sequential circuit?
20. What do we mean when we say that a sequential circuit is edge triggered rather than level triggered?
21. In the context of digital circuits, what is feedback?
22. How is a JK flip-flop related to an SR flip-flop?
23. Why are JK flip-flops often preferred to SR flip-flops?
24. Which flip-flop gives a true representation of computer memory?
25. How is a Mealy machine different from a Moore machine?
26. What does an algorithmic state machine offer that is not provided by either a Moore or a Mealy machine?
Construct a truth table for the following:a) yz + z(xy)′b) x(y′ + z) + xyzc) (x + y)(x′ + y) (Hint: This is from Example 3.7.)
Construct a truth table for the following:a) xyz + x(yz)′ + x′(y + z) + (xyz)′b) (x + y′)(x′ + z′)(y′ + z′)
Using DeMorgan’s Law, write an expression for the complement of F if F(x, y, z) = xy′(x + z).
Using DeMorgan’s Law, write an expression for the complement of F if F (x, y, z) = (x′ + y)(x + z)(y′ + z)′.
5. Using DeMorgan’s Law, write an expression for the complement of F if F (w, x, y, z) = xz′(x′yz + x) + y(w′z + x′).
6. Using DeMorgan’s Law, write an expression for the complement of F if F (x, y, z) = xz′(xy + xz) + xy′(wz + y).
7. Prove that DeMorgan’s Laws are valid.
8. Is the following distributive law valid or invalid? Prove your answer.x XOR (y + z) = (x XOR y) + (x XOR z)
9. Is the following true or false? Prove your answer.(x XOR y)′ = xy + (x + y)′
10. Show that x = xy + xy′a) Using truth tablesb) Using Boolean identities
11. Use only the first seven Boolean identities to prove the Absorption Laws.
12. Show that xz = (x + y)(x + y′)(x′ + z)a) Using truth tablesb) Using Boolean identities
13. Use any method to prove the following either true or false.xz + x′y′ + y′z′ = xz + y′
14. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.a) F(x, y, z) = y (x′ + (x + y)′)b) F (x, y, z) = x ′yz + xzc) F
15. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.a) x(yz + y′z) + xy + x′y + xzb) xyz′′ + (y + z)′ + x′yzc)
16. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.a) z (w + x)′ + w′xz + wxyz′ + wx′yz′b) y′(x′z′ + xz) +
17. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.a) x(y + z)(x′ + z′)b) xy + xyz + xy′z + x′y′zc) xy′z + x(y
18. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step.a) y(xz′ + x′z) + y′(xz′ + x′z)b) x(y′z + y) + x′(y +
19. Using the basic identities of Boolean algebra, show that x(x′ + y) = xy
20. Using the basic identities of Boolean algebra, show that x + x′y = x + y
21. Using the basic identities of Boolean algebra, show that xy + x ′z + yz = xy + x ′z
22. The truth table for a Boolean expression is shown below.Write the Boolean expression in sum-of-products form. X 0 y 0 N 0 F 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1
23. The truth table for a Boolean expression is shown below. Write the Boolean expression in sum-of-products form. X y 0 N 0 F 1 0 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0
24. Which of the following Boolean expressions is not logically equivalent to all the rest?a) wx′ + wy′ + wzb) w + x′ + y′ + zc) w(x′ + y′ + z)c) wx′yz′ + wx′y′ + wy′z′ + wz
25. Draw the truth table and rewrite the expression below as the complemented sum of two products:xy′ + x′y + xz + y′z
26. Given the Boolean function, F(x, y, z) = x′y + xyz′a) Derive an algebraic expression for the complement of F.Express in sum-of-products form.b) Show that FF′. = 0.c) Show that F + F′ = 1.
27. Given the function, F (x, y, z) = y(x′z + xz′) + x(yz + yz′)a) List the truth table for F.b) Draw the logic diagram using the original Boolean expression.c) Simplify the expression using
28. Write a simplified expression for the Boolean function defined by each of the following Kmaps:a) 2. yz 00 00 01 11 10 0 0 1 1 0 1 1 0 0 1 b) yz 00 00 01 11 10 0 0 1 1 1 1 1 0 0 0 3. c) yz X 00 00
29. Write a simplified expression for the Boolean function defined by each of the following Kmaps: 1. a) yz X 00 00 01 11 10 0 1 1 1 1 1 1 0 0 0 2. b) X yz 00 00 01 11 10 0 1 0 0 1 1 1 0 0 0 3. c) yz
30. Create the Kmaps and then simplify for the following functions:a) F(x, y, z) = x′y′z′ + x′yz + x′yz′b) F(x, y, z) = x′y′z′ + x′yz′ + xy′z′ + xyz′c) F(x, y, z) =
31. Write a simplified expression for the Boolean function defined by each of the following Kmaps: 1. WX yz 2. b) 00 00 01 00 00 1 11 10 10 0 1 01 1 0 0 1 11 0 0 1 0 10 1 0 1 0 yz WX 00 00 01 11 10
32. Write a simplified expression for the Boolean function defined by each of the following Kmaps (leave in sum-of-products form): 1. a) WX yz 2. b) 00 01 11 10 00 1 1 0 1 01 1 1 0 1 11 0 0 0 0 10 10
33. Create the Kmaps and then simplify for the following functions (leave in sum-of-products form):a) F(w, x, y, z) = w′x′y′z′ + w′x′yz′ + w′xy′z + w′xyz + w′xyz′ +
34. Create the Kmaps and then simplify for the following functions (leave in sum-of-products form):a) F(w, x, y, z) = w′x′y′z + w′x′yz′ + w′xy′z + w′xyz + w′xyz′ + wxy′z +
35. Given the following Kmap, show algebraically (using Boolean identities) how the four terms reduce to one term. yz 00 01 11 10 0 0 1 1 0 1 0 1 1 0
36. Write a simplified expression for the Boolean function defined by each of the following Kmaps: 1. a) X yz 00 00 01 11 10 0 1 1 0 X 1 1 1 1 1 2. b)
37. Write a simplified expression for the Boolean function defined by each of the following Kmaps: 1. a) X yz 00 00 01 11 10 0 X 0 0 1 1 1 1 X 1 2. b) yz WX 00 00 01 11 10 00 1 1 1 1 01 X 0 1 X 11 0
38. Write a simplified expression for the Boolean function defined by each of the following Kmaps: 1. a) X yz 0 00 00 01 1 11 0 10 1 1 0 0 1 1 2. b) yz WX 00 01 11 10 00 0 0 1 0 50 01 X 0 0 X 11 X 1
39. Find the minimized Boolean expression for the functions defined by each of the following truth tables: 1. a) X y N F 0 X 0 0 1 X 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1
40. Construct the XOR operator using only AND, OR, and NOT gates.
41. Construct the XOR operator using only NAND gates. Hint:x XOR y = ((x′y)′(xy′)′)′
42. Draw a half-adder using only NAND gates.
43. Draw a full-adder using only NAND gates.
44. Design a circuit with three inputs x, y, and z representing the bits in a binary number, and three outputs (a,b, andc) also representing bits in a binary number. When the input is 0, 1, 6, or 7,
45. Draw the combinational circuit that directly implements the Boolean expression:F(x, y, z) = xyz + (y′ + z)
46. Draw the combinational circuit that directly implements the following Boolean expression:F(x, y, z) = x + xy + y′z
47. Draw the combinational circuit that directly implements the Boolean expression:F(x, y, z) = (x(yXORz)) + (xz)′
48. Find the truth table that describes the following circuit: N F X
49. Find the truth table that describes the following circuit: y N X F
50. Find the truth table that describes the following circuit: X. N D F
51. How many inputs does a decoder have if it has 64 outputs?
52. How many control lines does a multiplexer have if it has 32 inputs?
53. Draw circuits to implement the parity generator and parity checker shown in Tables 3.10 and 3.11, respectively.
54. Assume you have the following truth tables for functions F (x, y, z) and F (x, y, z):a) Express F and F in sum-of-products form.b) Simplify each function.c) Draw one logic circuit to implement
55. Assume you have the following truth tables for functions F (w, x, y, z) and F (w, x, y, z):a) Express F and F in sum-of-products form.b) Simplify each function.c) Draw one logic circuit to
57. Simplify the function from exercise 56 and draw the logic circuit.
59. Little Susie is trying to train her new puppy. She is trying to figure out when the puppy should get a dog biscuit as a reward. She has concluded the following:Give the puppy a biscuit if it sits
60. Tyrone Shoelaces has invested a huge amount of money into the stock market and doesn’t trust just anyone to give him buying and selling information. Before he will buy a certain stock, he must
62. Complete the truth table for the following sequential circuit: X Y 0 0 AD 0 X J Q D Q B 0 0 1 0 1 Y K Q' 0 Q' 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Next State A B
63. Complete the truth table for the following sequential circuit: X D Next State A A B x A B B 0 0 C 0 0 1 J 0 0 1 0 0 1 1 Q' K Q' 1 0 0 1 0 1 1 1 0 1 1 1
64. Complete the truth table for the following sequential circuit: x- D Q' A B AO 0 0 BOO XO 0 1 0 lolo 1 0 0 1 1 1 1 1 101 0 1 0 1 1 1 Next State A B
65. Complete the truth table for the following sequential circuit: X D Q Q' Next State A 0 0 BOO X A B 0 0 0 1 J Q B 0 1 0 KQ 0 1 1 1 0 0 lo 1 0 1 1 1 0 1 1 1

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