# Final Exam -- Open Book Section

10 May, 1994

The entire exam is to be turned in at 8:30 PM. Work the closed book section first and turn it in before you consult your books and notes to work on the open book section.

## Problem 1. (12 points)

The state table for a sequential circuit with one state variable, A, two inputs x and y, and one output z, is shown in the five leftmost columns of the following table. Fill in the two righmost columns of the table with the appropriate inputs for a JK flip-flop implementing these state transitions

```    present      inputs       next   output     Flip-flop
state                   state               inputs
A       x       y       A       z       JA      JB
0       0       0       0       0
0       0       1       0       0
0       1       0       0       0
0       1       1       1       0
1       0       0       0       1
1       0       1       0       0
1       1       0       0       0
1       1       1       1       0
```

Now, derive minimal sum-of-product implementation for the two inputs, JA and KA, to the A flip-flop and for the output z.

• JA =
• KA =
• z =

## Problem 2. (3 points)

Convert the hexadecimal number A8BE42 to binary and octal.

## Problem 3. (6 points)

Represent the decimal number 16.75 as a floating-point number with 32 bits. The normalized mantissa has 23 bits, the exponenthas 8 bits, and there is a 1 bit sign. Be sure to show how you got your answer!

## Problem 4. (9 points)

Show the hardware needed to implement the following RTL statements for eight-bit registers R1 and R2 and control inputs p and q.

• p : R1 <- R2
• p q : R2 <- R1
• p' q : R2 <- R2+1

## Problem 5. (6 points)

Assuming the following values for eight bit registers R1 and R2

• R1 = 01001100
• R2 = 11100101

What are the values of the following expressions

• R1 - R2
• R1 XOR R2
• ashl R

ashl is arithmetic left shift.

## Problem 6. (3 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?

• IR <- M[AR]>, DR <- 0

## Problem 7. (6 points)

Here is a typical ``solution'' turned in last week for implementing the ADM instruction described in problem 7-16 (p. 237):

```          ORG  24
ACTDR          U    JMP  NEXT
WRITE          U    JMP  FETCH
```

Although this micro-code routine sets M[EA] to M[EA]+AC, it modifies the value of AC when it shouldn't. Fix the routine so that the value of AC is unchanged by the ADM instruction.

## Problem 8. (3 points)

Translate the following expression into reverse Polish notation (RPN):

• A + E * (F + G) + B

## Problem 9. (12 points)

Show how to compute the following Pascal statements

```     IF x = 7 THEN
x := 0
ELSE
x := x + 1 ;
y := 2 * x ;
```

using the assembly language of the textbook.