# Final exam for CSCI 274

This is an open book, open notes exam; however, the use of calculators is forbidden. The exam is to be turned in by 8:30 PM.

## Problem 1. (10 points)

Convert the following decimal numbers into 10-bit two's-complement binary numbers

• -47
• 113

## Problem 2. (10 points)

Represent the following 10-bit two's-complement numbers as decimal numbers

• 1100111001
• 0000111100

## Problem 3. (10 points)

Convert the decimal number 6.65 into a floating point number with one sign bit, an eight-bit exponent expressed using excess-127 notation, and a 23-bit mantissa. By the way, if it takes you a long time to derive the mantissa, you are doing something wrong.

## Problem 4. (10 points)

Use either a truth table or Boolean algebra to show that the following two Boolean expressions are equivalent:

• A ( A + B' C + A' ) + B
• A + B

## Problem 5. (10 points)

Draw a sum-of-products circuit implementation of the following Boolean expression

• ( x + y ) z'

## Problem 6. (10 points)

Now implement the Boolean expression, ( x + y ) z', of the previous problem using only four two-input NAND gates. Hint: Start with the sum-of-products implementation.

## Problem 7. (10 points)

If registers A and B have the following values:

• A = 0011001010
• B = 1000101110

what are the values of the following five expressions

 A + B + is ordinary addition A - B - is ordinary addition A AND B AND is bit-wise logical and, C's & operator, the upside-down V asl B asl is arithmetic shift left csl B csl is circular shift left

## Problem 8. (10 points)

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

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

what happens in the next bus transaction?

## Problem 9. (10 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?

• TR <- M[AR], PC <- M[AR], DR <- 0

## Problem 10. (10 points)

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

• 2500
• 7400
• 7080
• 3500
• 2500

What action is performed when these five words are executed in order?