Final Exam -- 12 December, 1995

Problem 1. (4 points)

Convert the decimal number 89 into a binary number.

Problem 2. (4 points)

Convert the binary number 110110011 into a decimal number.

Problem 3. (4 points)

Represent the decimal number -100 as a twelve-bit two's complement binary number .

Problem 4. (8 points)

Convert the decimal number 14.62 into a floating point number with one sign bit, an eight-bit exponent expressed using excess-127 notation, and a 23-bit mantissa.

Problem 5. (8 points)

Use truth tables to show that the following two Boolean expressions are equivalent:

• A (A C + A' C) (B + C)
• A C

Problem 6. (8 points)

Now, simplify the following Boolean expression, from the previous problem, using Boolean algebra. It is very important to show your work!

• A (A C + A' C) (B + C)

Problem 7. (8 points)

Simplify the following Boolean function using a Karnaugh map. Notice the don't care conditions!

• F(a, b, c, d) = Sigma(1, 4, 7, 9, 10, 14)
• F(a, b, c, d) = d(3, 8, 11, 13, 15)

Problem 8. (3 points)

How many different values can be stored in an eight-bit register.

Problem 9. (3 points)

Draw the symbol used in diglog to represent an input pad, the thing your mashed to generate a zero or one, in the space below.

Problem 10. (10 points)

If registers S and T have the following values:

• S = 0011110011
• T = 1111100000

what are their values after each of the following RTL statements are performed

• S <- S and T, T <- S-T
• T <- asl S

where asl is the arithmetic shift left operator.

Problem 11. (8 points)

Show the hardware needed to implement the following RTL statements for eight-bit registers A and B:

• p: A <- A+1, B <- A
• q r: A <- A-1

You may use eight-bit adders, eight-bit multiplexers, eight-bit registers, and assorted logic gates in your solution.

Problem 12. (5 points)

Look at Figure 5-4 on page 130 of the textbook, if

• S2 S1 S0 = 001
• LD of IR is set
• LD of PC is set
• INR of DR is set

what happens in the next bus transaction?

Problem 13. (5 points)

How would you set the control inputs of the bus system shown in Figure 5-4 on page 130 of the textbook to execute the following RTL statement?

• M[AR] <- DR, DR <- 0

Problem 14. (5 points)

Suppose the following 16 bits hexadecimal values is stored in the memory of the "basic computer" described in Table 5-2 on page 133 of the textbook.

• A200

What action is performed when this word in executed as an instruction?

Problem 15. (5 points)

Do you think there are more microcode programmers than assembly language programmers? Justify your answer.

Problem 16. (12 points)

Write a procedure in the textbook's assembly language, using the calling conventions described in Section 6-7 (pp. 200-202), equivalent to the following C subroutine

     int useless(int a)
       {
        if (a & 1)
           return(a) ;
        else
           return(a+1) ;
       }

Hint for the non-C experts: This function returns a, if a is odd, and a+1, if a is even.

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