Final Exam -- Open book section

8 May, 1995

Problem 1. (8 points)

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

• x + z(x' + x y') + y
• x + y + z

Problem 2. (8 points)

Simplify the following two Boolean expressions using Boolean algebra.

• x + z(x' + x y') + y
• (A' B')' + A' B + A B'

Problem 3. (4 points)

In the space below, show how to implement an OR gate using one NAND and two inverters.

Problem 4. (4 points)

Convert the decimal number 5.3125 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)

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

• p' : R <- R - 1
• p q : R <- 0, S <- R

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

Problem 6. (4 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?

• AR <- M[AR], PC <- PC+1

Problem 7. (6 points)

Suppose that the basic computer of table 5-6 (page 159) is modified by replaced the BSA instruction with an XCH instruction that performs the following operations

• AC <- M[EA], M[EA] <- AC

Show how the RTL specification of the machine must be changed to implement this change.
[This is part of Problem 5-13 for page 169 of the textbook.]

Problem 8. (8 points)

Write a subroutine in the assembly language of the book (Chapter 6) that receives a single argument stored in the accumulator and returns, in the accumulator, that argument multiplied by 16. By the way, the easy way to multiply a value by 16 is to left shift is four times. To help you out, I've provided the first word of the subroutine.

     M16,      HEX  0

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